LMFDB - Embedded newform 875.2.bb.b.857.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			857.9
Character	$\chi$	$=$	875.857
Dual form			875.2.bb.b.243.9

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.263087 + 0.0137878i) q^{2} +(1.61063 - 1.98896i) q^{3} +(-1.92002 + 0.201802i) q^{4} +(-0.396312 + 0.545476i) q^{6} +(2.51572 + 0.819241i) q^{7} +(1.02276 - 0.161989i) q^{8} +(-0.738101 - 3.47249i) q^{9} +(-3.43661 - 0.730475i) q^{11} +(-2.69106 + 4.14386i) q^{12} +(-3.27037 + 1.66634i) q^{13} +(-0.673149 - 0.180846i) q^{14} +(3.50997 - 0.746068i) q^{16} +(2.11271 - 5.50381i) q^{17} +(0.242063 + 0.903391i) q^{18} +(0.817063 - 7.77383i) q^{19} +(5.68132 - 3.68417i) q^{21} +(0.914201 + 0.144795i) q^{22} +(-0.334690 - 6.38626i) q^{23} +(1.32509 - 2.29513i) q^{24} +(0.837417 - 0.483483i) q^{26} +(-1.25435 - 0.639125i) q^{27} +(-4.99555 - 1.06528i) q^{28} +(-0.147381 - 0.202852i) q^{29} +(0.511405 + 1.14863i) q^{31} +(-2.91359 + 0.780694i) q^{32} +(-6.98798 + 5.65876i) q^{33} +(-0.479943 + 1.47711i) q^{34} +(2.11792 + 6.51830i) q^{36} +(-4.12728 - 2.68029i) q^{37} +(-0.107775 + 2.05646i) q^{38} +(-1.95307 + 9.18847i) q^{39} +(0.567075 + 0.184254i) q^{41} +(-1.44389 + 1.04759i) q^{42} +(-5.65218 + 5.65218i) q^{43} +(6.74578 + 0.709010i) q^{44} +(0.176105 + 1.67553i) q^{46} +(0.980249 - 0.376282i) q^{47} +(4.16936 - 8.18282i) q^{48} +(5.65769 + 4.12196i) q^{49} +(-7.54405 - 13.0667i) q^{51} +(5.94290 - 3.85937i) q^{52} +(-2.30142 - 1.86365i) q^{53} +(0.338816 + 0.150851i) q^{54} +(2.70568 + 0.430367i) q^{56} +(-14.1458 - 14.1458i) q^{57} +(0.0415708 + 0.0513357i) q^{58} +(-3.73669 - 4.15002i) q^{59} +(2.91370 + 2.62351i) q^{61} +(-0.150381 - 0.295140i) q^{62} +(0.987952 - 9.34049i) q^{63} +(-6.06975 + 1.97218i) q^{64} +(1.76043 - 1.58510i) q^{66} +(-1.10691 - 0.424905i) q^{67} +(-2.94577 + 10.9938i) q^{68} +(-13.2411 - 9.62020i) q^{69} +(7.13505 - 5.18392i) q^{71} +(-1.31741 - 3.43196i) q^{72} +(4.36627 + 6.72347i) q^{73} +(1.12279 + 0.648243i) q^{74} +15.0908i q^{76} +(-8.04712 - 4.65309i) q^{77} +(0.387139 - 2.44430i) q^{78} +(4.00368 - 8.99240i) q^{79} +(6.43796 - 2.86636i) q^{81} +(-0.151731 - 0.0406561i) q^{82} +(0.951116 + 6.00511i) q^{83} +(-10.1648 + 8.22017i) q^{84} +(1.40908 - 1.56495i) q^{86} +(-0.640839 - 0.0335849i) q^{87} +(-3.63316 - 0.190406i) q^{88} +(2.57386 - 2.85856i) q^{89} +(-9.59246 + 1.51281i) q^{91} +(1.93137 + 12.1942i) q^{92} +(3.10827 + 0.832857i) q^{93} +(-0.252703 + 0.112511i) q^{94} +(-3.13994 + 7.05242i) q^{96} +(-1.59410 + 10.0647i) q^{97} +(-1.54530 - 1.00643i) q^{98} +12.4728i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 2 q^{2} + 6 q^{3} + 10 q^{4} - 10 q^{7} + 64 q^{8} + 10 q^{9} - 6 q^{11} - 6 q^{12} + 20 q^{14} - 30 q^{16} - 12 q^{17} - 14 q^{18} + 30 q^{19} - 12 q^{21} - 8 q^{22} + 30 q^{23} - 48 q^{26} - 58 q^{28}+ \cdots + 62 q^{98}+O(q^{100}) $ 288 * q + 2 * q^2 + 6 * q^3 + 10 * q^4 - 10 * q^7 + 64 * q^8 + 10 * q^9 - 6 * q^11 - 6 * q^12 + 20 * q^14 - 30 * q^16 - 12 * q^17 - 14 * q^18 + 30 * q^19 - 12 * q^21 - 8 * q^22 + 30 * q^23 - 48 * q^26 - 58 * q^28 - 18 * q^31 + 8 * q^32 - 150 * q^33 + 40 * q^36 + 12 * q^38 - 30 * q^39 + 166 * q^42 - 108 * q^43 + 10 * q^44 - 6 * q^46 - 24 * q^47 - 16 * q^51 - 24 * q^52 - 40 * q^53 + 30 * q^54 + 4 * q^56 - 216 * q^57 - 114 * q^58 - 90 * q^59 - 18 * q^61 - 16 * q^63 + 100 * q^64 - 90 * q^66 + 74 * q^67 + 342 * q^68 - 24 * q^71 - 222 * q^72 - 216 * q^73 + 90 * q^77 - 32 * q^78 + 10 * q^79 - 10 * q^81 + 216 * q^82 - 20 * q^84 - 6 * q^86 - 18 * q^87 + 58 * q^88 - 120 * q^89 - 12 * q^91 - 24 * q^92 + 106 * q^93 + 30 * q^94 - 90 * q^96 + 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.263087	+	0.0137878i	−0.186031	+	0.00974946i	−0.145124	−	0.989413i	$-0.546358\pi$
$2$	−0.263087	+	0.0137878i	−0.186031	+	0.00974946i	−0.0409070	+	0.999163i	$0.513025\pi$
$3$	1.61063	−	1.98896i	0.929895	−	1.14833i	−0.0587824	−	0.998271i	$-0.518722\pi$
$3$	1.61063	−	1.98896i	0.929895	−	1.14833i	0.988678	−	0.150054i	$-0.0479448\pi$
$4$	−1.92002	+	0.201802i	−0.960009	+	0.100901i
$5$		0			0
$5$		0			0
$6$	−0.396312	+	0.545476i	−0.161794	+	0.222690i
$7$	2.51572	+	0.819241i	0.950853	+	0.309644i
$7$	2.51572	+	0.819241i	0.950853	+	0.309644i
$8$	1.02276	−	0.161989i	0.361600	−	0.0572718i
$9$	−0.738101	−	3.47249i	−0.246034	−	1.15750i
$10$		0			0
$11$	−3.43661	−	0.730475i	−1.03618	−	0.220246i	−0.341737	−	0.939796i	$-0.611015\pi$
$11$	−3.43661	−	0.730475i	−1.03618	−	0.220246i	−0.694441	+	0.719549i	$0.744348\pi$
$12$	−2.69106	+	4.14386i	−0.776841	+	1.19623i
$13$	−3.27037	+	1.66634i	−0.907037	+	0.462159i	−0.844300	−	0.535871i	$-0.819983\pi$
$13$	−3.27037	+	1.66634i	−0.907037	+	0.462159i	−0.0627378	+	0.998030i	$0.519983\pi$
$14$	−0.673149	−	0.180846i	−0.179907	−	0.0483330i
$15$		0			0
$16$	3.50997	−	0.746068i	0.877493	−	0.186517i
$17$	2.11271	−	5.50381i	0.512408	−	1.33487i	−0.396561	−	0.918008i	$-0.629797\pi$
$17$	2.11271	−	5.50381i	0.512408	−	1.33487i	0.908970	−	0.416862i	$-0.136870\pi$
$18$	0.242063	+	0.903391i	0.0570548	+	0.212931i
$19$	0.817063	−	7.77383i	0.187447	−	1.78344i	−0.346628	−	0.938003i	$-0.612673\pi$
$19$	0.817063	−	7.77383i	0.187447	−	1.78344i	0.534075	−	0.845437i	$-0.320660\pi$
$20$		0			0
$21$	5.68132	−	3.68417i	1.23977	−	0.803951i
$22$	0.914201	+	0.144795i	0.194908	+	0.0308704i
$23$	−0.334690	−	6.38626i	−0.0697877	−	1.33163i	−0.779174	−	0.626808i	$-0.784361\pi$
$23$	−0.334690	−	6.38626i	−0.0697877	−	1.33163i	0.709386	−	0.704820i	$-0.248972\pi$
$24$	1.32509	−	2.29513i	0.270484	−	0.468491i
$25$		0			0
$26$	0.837417	−	0.483483i	0.164231	−	0.0948189i
$27$	−1.25435	−	0.639125i	−0.241400	−	0.123000i
$28$	−4.99555	−	1.06528i	−0.944071	−	0.201319i
$29$	−0.147381	−	0.202852i	−0.0273679	−	0.0376687i	0.795114	−	0.606460i	$-0.207411\pi$
$29$	−0.147381	−	0.202852i	−0.0273679	−	0.0376687i	−0.822482	+	0.568792i	$0.807411\pi$
$30$		0			0
$31$	0.511405	+	1.14863i	0.0918510	+	0.206301i	0.953629	−	0.300985i	$-0.0973155\pi$
$31$	0.511405	+	1.14863i	0.0918510	+	0.206301i	−0.861778	+	0.507286i	$0.830649\pi$
$32$	−2.91359	+	0.780694i	−0.515055	+	0.138009i
$33$	−6.98798	+	5.65876i	−1.21645	+	0.985063i
$34$	−0.479943	+	1.47711i	−0.0823095	+	0.253323i
$35$		0			0
$36$	2.11792	+	6.51830i	0.352987	+	1.08638i
$37$	−4.12728	−	2.68029i	−0.678520	−	0.440636i	0.158828	−	0.987306i	$-0.449229\pi$
$37$	−4.12728	−	2.68029i	−0.678520	−	0.440636i	−0.837348	+	0.546670i	$0.815895\pi$
$38$	−0.107775	+	2.05646i	−0.0174834	+	0.333602i
$39$	−1.95307	+	9.18847i	−0.312741	+	1.47133i
$40$		0			0
$41$	0.567075	+	0.184254i	0.0885622	+	0.0287756i	0.352963	−	0.935637i	$-0.385174\pi$
$41$	0.567075	+	0.184254i	0.0885622	+	0.0287756i	−0.264401	+	0.964413i	$0.585174\pi$
$42$	−1.44389	+	1.04759i	−0.222796	+	0.161647i
$43$	−5.65218	+	5.65218i	−0.861949	+	0.861949i	−0.991564	−	0.129616i	$-0.958626\pi$
$43$	−5.65218	+	5.65218i	−0.861949	+	0.861949i	0.129616	+	0.991564i	$0.458626\pi$
$44$	6.74578	+	0.709010i	1.01696	+	0.106887i
$45$		0			0
$46$	0.176105	+	1.67553i	0.0259653	+	0.247043i
$47$	0.980249	−	0.376282i	0.142984	−	0.0548864i	−0.285824	−	0.958282i	$-0.592267\pi$
$47$	0.980249	−	0.376282i	0.142984	−	0.0548864i	0.428808	+	0.903396i	$0.358934\pi$
$48$	4.16936	−	8.18282i	0.601795	−	1.18109i
$49$	5.65769	+	4.12196i	0.808241	+	0.588852i
$50$		0			0
$51$	−7.54405	−	13.0667i	−1.05638	−	1.82970i
$52$	5.94290	−	3.85937i	0.824132	−	0.535198i
$53$	−2.30142	−	1.86365i	−0.316124	−	0.255992i	0.458104	−	0.888898i	$-0.348529\pi$
$53$	−2.30142	−	1.86365i	−0.316124	−	0.255992i	−0.774229	+	0.632906i	$0.781862\pi$
$54$	0.338816	+	0.150851i	0.0461071	+	0.0205282i
$55$		0			0
$56$	2.70568	+	0.430367i	0.361562	+	0.0575103i
$57$	−14.1458	−	14.1458i	−1.87366	−	1.87366i
$58$	0.0415708	+	0.0513357i	0.00545852	+	0.00674071i
$59$	−3.73669	−	4.15002i	−0.486476	−	0.540286i	0.449068	−	0.893498i	$-0.351756\pi$
$59$	−3.73669	−	4.15002i	−0.486476	−	0.540286i	−0.935543	+	0.353212i	$0.885090\pi$
$60$		0			0
$61$	2.91370	+	2.62351i	0.373062	+	0.335906i	0.834240	−	0.551401i	$-0.185907\pi$
$61$	2.91370	+	2.62351i	0.373062	+	0.335906i	−0.461179	+	0.887307i	$0.652573\pi$
$62$	−0.150381	−	0.295140i	−0.0190984	−	0.0374828i
$63$	0.987952	−	9.34049i	0.124470	−	1.17679i
$64$	−6.06975	+	1.97218i	−0.758719	+	0.246523i
$65$		0			0
$66$	1.76043	−	1.58510i	0.216694	−	0.195112i
$67$	−1.10691	−	0.424905i	−0.135231	−	0.0519104i	0.289811	−	0.957084i	$-0.406407\pi$
$67$	−1.10691	−	0.424905i	−0.135231	−	0.0519104i	−0.425042	+	0.905173i	$0.639741\pi$
$68$	−2.94577	+	10.9938i	−0.357227	+	1.33319i
$69$	−13.2411	−	9.62020i	−1.59404	−	1.15814i
$70$		0			0
$71$	7.13505	−	5.18392i	0.846775	−	0.615218i	−0.0774798	−	0.996994i	$-0.524687\pi$
$71$	7.13505	−	5.18392i	0.846775	−	0.615218i	0.924255	+	0.381776i	$0.124687\pi$
$72$	−1.31741	−	3.43196i	−0.155258	−	0.404460i
$73$	4.36627	+	6.72347i	0.511034	+	0.786923i	0.996163	−	0.0875197i	$-0.0278941\pi$
$73$	4.36627	+	6.72347i	0.511034	+	0.786923i	−0.485129	+	0.874443i	$0.661227\pi$
$74$	1.12279	+	0.648243i	0.130522	+	0.0753567i
$75$		0			0
$76$			15.0908i			1.73103i
$77$	−8.04712	−	4.65309i	−0.917055	−	0.530268i
$78$	0.387139	−	2.44430i	0.0438348	−	0.276762i
$79$	4.00368	−	8.99240i	0.450449	−	1.01172i	−0.535478	−	0.844549i	$-0.679869\pi$
$79$	4.00368	−	8.99240i	0.450449	−	1.01172i	0.985927	−	0.167176i	$-0.0534647\pi$
$80$		0			0
$81$	6.43796	−	2.86636i	0.715329	−	0.318485i
$82$	−0.151731	−	0.0406561i	−0.0167558	−	0.00448972i
$83$	0.951116	+	6.00511i	0.104399	+	0.659146i	0.983279	+	0.182105i	$0.0582909\pi$
$83$	0.951116	+	6.00511i	0.104399	+	0.659146i	−0.878881	+	0.477042i	$0.841709\pi$
$84$	−10.1648	+	8.22017i	−1.10907	+	0.896895i
$85$		0			0
$86$	1.40908	−	1.56495i	0.151945	−	0.168753i
$87$	−0.640839	−	0.0335849i	−0.0687051	−	0.00360068i
$88$	−3.63316	−	0.190406i	−0.387296	−	0.0202973i
$89$	2.57386	−	2.85856i	0.272829	−	0.303007i	−0.591123	−	0.806581i	$-0.701315\pi$
$89$	2.57386	−	2.85856i	0.272829	−	0.303007i	0.863952	+	0.503574i	$0.167982\pi$
$90$		0			0
$91$	−9.59246	+	1.51281i	−1.00556	+	0.158586i
$92$	1.93137	+	12.1942i	0.201360	+	1.27133i
$93$	3.10827	+	0.832857i	0.322312	+	0.0863633i
$94$	−0.252703	+	0.112511i	−0.0260643	+	0.0116046i
$95$		0			0
$96$	−3.13994	+	7.05242i	−0.320469	+	0.719784i
$97$	−1.59410	+	10.0647i	−0.161856	+	1.02192i	0.764323	+	0.644834i	$0.223073\pi$
$97$	−1.59410	+	10.0647i	−0.161856	+	1.02192i	−0.926179	+	0.377085i	$0.876927\pi$
$98$	−1.54530	−	1.00643i	−0.156099	−	0.101665i
$99$			12.4728i			1.25356i
$100$		0			0
$101$	9.38700	+	5.41959i	0.934041	+	0.539269i	0.888087	−	0.459675i	$-0.152034\pi$
$101$	9.38700	+	5.41959i	0.934041	+	0.539269i	0.0459539	+	0.998944i	$0.485367\pi$
$102$	2.16490	+	3.33366i	0.214357	+	0.330082i
$103$	−1.76689	−	4.60289i	−0.174096	−	0.453537i	0.818572	−	0.574403i	$-0.194766\pi$
$103$	−1.76689	−	4.60289i	−0.174096	−	0.453537i	−0.992669	+	0.120867i	$0.961433\pi$
$104$	−3.07487	+	2.23403i	−0.301516	+	0.219064i
$105$		0			0
$106$	0.631170	+	0.458572i	0.0613046	+	0.0445404i
$107$	−2.23275	+	8.33275i	−0.215848	+	0.805557i	0.770018	+	0.638022i	$0.220247\pi$
$107$	−2.23275	+	8.33275i	−0.215848	+	0.805557i	−0.985866	+	0.167535i	$0.946419\pi$
$108$	2.53736	+	0.974000i	0.244157	+	0.0937232i
$109$	6.47269	−	5.82804i	0.619972	−	0.558225i	−0.298152	−	0.954518i	$-0.596370\pi$
$109$	6.47269	−	5.82804i	0.619972	−	0.558225i	0.918124	+	0.396293i	$0.129704\pi$
$110$		0			0
$111$	−11.9785	+	3.89204i	−1.13695	+	0.369416i
$112$	9.44131	+	0.998616i	0.892120	+	0.0943604i
$113$	3.59375	+	7.05314i	0.338072	+	0.663504i	0.995978	−	0.0895963i	$-0.0285577\pi$
$113$	3.59375	+	7.05314i	0.338072	+	0.663504i	−0.657906	+	0.753100i	$0.728558\pi$
$114$	3.91663	+	3.52655i	0.366826	+	0.330292i
$115$		0			0
$116$	0.323909	+	0.359738i	0.0300742	+	0.0334008i
$117$	8.20020	+	10.1264i	0.758109	+	0.936186i
$118$	1.04030	+	1.04030i	0.0957670	+	0.0957670i
$119$	9.82394	−	12.1152i	0.900559	−	1.11060i
$120$		0			0
$121$	1.22772	+	0.546618i	0.111611	+	0.0496925i
$122$	−0.802731	−	0.650039i	−0.0726759	−	0.0588517i
$123$	1.27982	−	0.831124i	0.115397	−	0.0749399i
$124$	−1.21370	−	2.10220i	−0.108994	−	0.188783i
$125$		0			0
$126$	−0.131133	+	2.47099i	−0.0116822	+	0.220133i
$127$	4.46370	−	8.76051i	0.396090	−	0.777370i	−0.603714	−	0.797201i	$-0.706313\pi$
$127$	4.46370	−	8.76051i	0.396090	−	0.777370i	0.999803	+	0.0198315i	$0.00631297\pi$
$128$	7.20173	−	2.76449i	0.636549	−	0.244348i
$129$	2.13840	+	20.3455i	0.188275	+	1.79132i
$130$		0			0
$131$	−13.5234	−	1.42136i	−1.18154	−	0.124185i	−0.506683	−	0.862132i	$-0.669129\pi$
$131$	−13.5234	−	1.42136i	−1.18154	−	0.124185i	−0.674858	+	0.737947i	$0.735795\pi$
$132$	12.2751	−	12.2751i	1.06841	−	1.06841i
$133$	8.42415	−	18.8874i	0.730466	−	1.63775i
$134$	0.297074	+	0.0965251i	0.0256633	+	0.00833850i
$135$		0			0
$136$	1.26924	−	5.97131i	0.108837	−	0.512036i
$137$	−0.319201	+	6.09072i	−0.0272712	+	0.520365i	0.950504	+	0.310711i	$0.100567\pi$
$137$	−0.319201	+	6.09072i	−0.0272712	+	0.520365i	−0.977776	+	0.209654i	$0.932766\pi$
$138$	3.61620	+	2.34839i	0.307831	+	0.199908i
$139$	−0.132140	−	0.406687i	−0.0112080	−	0.0344947i	0.945296	−	0.326214i	$-0.105773\pi$
$139$	−0.132140	−	0.406687i	−0.0112080	−	0.0344947i	−0.956504	+	0.291719i	$0.905773\pi$
$140$		0			0
$141$	0.830405	−	2.55572i	0.0699327	−	0.215231i
$142$	−1.80567	+	1.46220i	−0.151528	+	0.122705i
$143$	12.4562	−	3.33763i	1.04164	−	0.279107i
$144$	−5.18142	−	11.6377i	−0.431785	−	0.969806i
$145$		0			0
$146$	−1.24141	−	1.70866i	−0.102740	−	0.141410i
$147$	17.3108	−	4.61396i	1.42777	−	0.380553i
$148$	8.46534	+	4.31331i	0.695847	+	0.354552i
$149$	2.78363	−	1.60713i	0.228044	−	0.131661i	−0.381626	−	0.924317i	$-0.624636\pi$
$149$	2.78363	−	1.60713i	0.228044	−	0.131661i	0.609669	+	0.792656i	$0.291302\pi$
$150$		0			0
$151$	2.73858	−	4.74335i	0.222862	−	0.386009i	−0.732814	−	0.680429i	$-0.761793\pi$
$151$	2.73858	−	4.74335i	0.222862	−	0.386009i	0.955676	+	0.294421i	$0.0951267\pi$
$152$	−0.423618	−	8.08312i	−0.0343600	−	0.655628i
$153$	−20.6713	−	3.27401i	−1.67118	−	0.264688i
$154$	2.18125	+	1.11322i	0.175770	+	0.0897054i
$155$		0			0
$156$	1.89568	−	18.0362i	0.151776	−	1.44405i
$157$	5.24342	+	19.5687i	0.418471	+	1.56175i	0.777781	+	0.628535i	$0.216345\pi$
$157$	5.24342	+	19.5687i	0.418471	+	1.56175i	−0.359310	+	0.933218i	$0.616988\pi$
$158$	−0.929331	+	2.42099i	−0.0739336	+	0.192604i
$159$	−7.41345	+	1.57578i	−0.587925	+	0.124967i
$160$		0			0
$161$	4.38990	−	16.3402i	0.345973	−	1.28779i
$162$	−1.65422	+	0.842869i	−0.129968	+	0.0662221i
$163$	−4.74149	+	7.30125i	−0.371382	+	0.571878i	−0.974112	−	0.226067i	$-0.927413\pi$
$163$	−4.74149	+	7.30125i	−0.371382	+	0.571878i	0.602730	+	0.797945i	$0.294080\pi$
$164$	−1.12598	−	0.239334i	−0.0879241	−	0.0186888i
$165$		0			0
$166$	−0.333024	−	1.56675i	−0.0258477	−	0.121604i
$167$	19.3182	−	3.05970i	1.49489	−	0.236767i	0.645182	−	0.764029i	$-0.276781\pi$
$167$	19.3182	−	3.05970i	1.49489	−	0.236767i	0.849703	+	0.527262i	$0.176781\pi$
$168$	5.21383	−	4.68833i	0.402256	−	0.361713i
$169$	0.277432	−	0.381852i	0.0213409	−	0.0293732i
$170$		0			0
$171$	−27.5976	+	2.90063i	−2.11044	+	0.221817i
$172$	9.71166	−	11.9929i	0.740507	−	0.914451i
$173$	8.38638	−	0.439511i	0.637604	−	0.0334154i	0.269205	−	0.963083i	$-0.413239\pi$
$173$	8.38638	−	0.439511i	0.637604	−	0.0334154i	0.368400	+	0.929668i	$0.379906\pi$
$174$	0.169060			0.0128164
$175$		0			0
$176$	−12.6074			−0.950319
$177$	−14.2726	+	0.747996i	−1.07280	+	0.0562229i
$178$	−0.637737	+	0.787540i	−0.0478004	+	0.0590286i
$179$	15.2840	−	1.60642i	1.14238	−	0.120069i	0.485623	−	0.874168i	$-0.338593\pi$
$179$	15.2840	−	1.60642i	1.14238	−	0.120069i	0.656761	+	0.754099i	$0.271926\pi$
$180$		0			0
$181$	−4.54675	+	6.25807i	−0.337957	+	0.465159i	−0.943843	−	0.330393i	$-0.892819\pi$
$181$	−4.54675	+	6.25807i	−0.337957	+	0.465159i	0.605886	+	0.795551i	$0.292819\pi$
$182$	2.50280	−	0.530261i	0.185520	−	0.0393056i
$183$	9.91094	−	1.56974i	0.732638	−	0.116038i
$184$	−1.37681	−	6.47740i	−0.101500	−	0.477520i
$185$		0			0
$186$	−0.829229	−	0.176258i	−0.0608020	−	0.0129239i
$187$	−11.2810	+	17.3712i	−0.824947	+	1.27031i
$188$	−1.80616	+	0.920285i	−0.131728	+	0.0671187i
$189$	−2.63200	−	2.63548i	−0.191450	−	0.191703i
$190$		0			0
$191$	6.76057	−	1.43700i	0.489178	−	0.103978i	0.0432821	−	0.999063i	$-0.486219\pi$
$191$	6.76057	−	1.43700i	0.489178	−	0.103978i	0.445896	+	0.895085i	$0.352885\pi$
$192$	−5.85351	+	15.2489i	−0.422441	+	1.10050i
$193$	−2.55619	−	9.53984i	−0.183999	−	0.686693i	−0.994843	−	0.101430i	$-0.967658\pi$
$193$	−2.55619	−	9.53984i	−0.183999	−	0.686693i	0.810844	−	0.585262i	$-0.199009\pi$
$194$	0.280616	−	2.66988i	0.0201470	−	0.191686i
$195$		0			0
$196$	−11.6947	−	6.77251i	−0.835335	−	0.483751i
$197$	−5.85802	−	0.927819i	−0.417367	−	0.0661044i	−0.0557804	−	0.998443i	$-0.517765\pi$
$197$	−5.85802	−	0.927819i	−0.417367	−	0.0661044i	−0.361586	+	0.932339i	$0.617765\pi$
$198$	−0.171972	−	3.28143i	−0.0122215	−	0.233201i
$199$	−0.710570	+	1.23074i	−0.0503709	+	0.0872450i	−0.890112	−	0.455743i	$-0.849374\pi$
$199$	−0.710570	+	1.23074i	−0.0503709	+	0.0872450i	0.839741	+	0.542988i	$0.182707\pi$
$200$		0			0
$201$	−2.62794	+	1.51724i	−0.185361	+	0.107018i
$202$	−2.54432	−	1.29640i	−0.179018	−	0.0912142i
$203$	−0.204584	−	0.631059i	−0.0143589	−	0.0442916i
$204$	17.1216	+	23.5659i	1.19875	+	1.64994i
$205$		0			0
$206$	0.528309	+	1.18660i	0.0368090	+	0.0826744i
$207$	−21.9292	+	5.87591i	−1.52418	+	0.408404i
$208$	−10.2357	+	8.28871i	−0.709719	+	0.574719i
$209$	−8.48652	+	26.1188i	−0.587025	+	1.80668i
$210$		0			0
$211$	4.15174	+	12.7778i	0.285818	+	0.879657i	0.986152	+	0.165842i	$0.0530341\pi$
$211$	4.15174	+	12.7778i	0.285818	+	0.879657i	−0.700335	+	0.713815i	$0.746966\pi$
$212$	4.79486	+	3.11382i	0.329312	+	0.213858i
$213$	1.18131	−	22.5407i	0.0809418	−	1.54446i
$214$	0.472518	−	2.22302i	0.0323007	−	0.151963i
$215$		0			0
$216$	−1.38643	−	0.450479i	−0.0943348	−	0.0306512i
$217$	0.345543	+	3.30861i	0.0234570	+	0.224603i
$218$	−1.62253	+	1.62253i	−0.109891	+	0.109891i
$219$	20.4051	+	2.14467i	1.37885	+	0.144923i
$220$		0			0
$221$	2.26184	+	21.5200i	0.152148	+	1.44759i
$222$	3.09772	−	1.18910i	0.207905	−	0.0798074i
$223$	−9.41051	+	18.4692i	−0.630175	+	1.23679i	0.326381	+	0.945238i	$0.394171\pi$
$223$	−9.41051	+	18.4692i	−0.630175	+	1.23679i	−0.956556	+	0.291549i	$0.905829\pi$
$224$	−7.96936	−	0.422925i	−0.532475	−	0.0282579i
$225$		0			0
$226$	−1.04272	−	1.80604i	−0.0693606	−	0.120136i
$227$	12.3279	−	8.00585i	0.818233	−	0.531367i	−0.0663243	−	0.997798i	$-0.521127\pi$
$227$	12.3279	−	8.00585i	0.818233	−	0.531367i	0.884557	+	0.466431i	$0.154461\pi$
$228$	30.0149	+	24.3056i	1.98779	+	1.60968i
$229$	18.2779	+	8.13786i	1.20784	+	0.537765i	0.909103	−	0.416571i	$-0.136768\pi$
$229$	18.2779	+	8.13786i	1.20784	+	0.537765i	0.298736	+	0.954336i	$0.403435\pi$
$230$		0			0
$231$	−22.2157	+	8.51100i	−1.46169	+	0.559983i
$232$	−0.183595	−	0.183595i	−0.0120536	−	0.0120536i
$233$	−4.30031	−	5.31044i	−0.281723	−	0.347899i	0.616567	−	0.787303i	$-0.288523\pi$
$233$	−4.30031	−	5.31044i	−0.281723	−	0.347899i	−0.898290	+	0.439404i	$0.855190\pi$
$234$	−2.29699	−	2.55106i	−0.150159	−	0.166768i
$235$		0			0
$236$	8.01200	+	7.21404i	0.521537	+	0.469594i
$237$	−11.4371	−	22.4465i	−0.742918	−	1.45806i
$238$	−2.41751	+	3.32281i	−0.156704	+	0.215386i
$239$	−4.07114	+	1.32279i	−0.263340	+	0.0855644i	−0.437711	−	0.899116i	$-0.644211\pi$
$239$	−4.07114	+	1.32279i	−0.263340	+	0.0855644i	0.174371	+	0.984680i	$0.444211\pi$
$240$		0			0
$241$	−2.71942	+	2.44858i	−0.175173	+	0.157727i	−0.752054	−	0.659102i	$-0.770937\pi$
$241$	−2.71942	+	2.44858i	−0.175173	+	0.157727i	0.576880	+	0.816829i	$0.304270\pi$
$242$	−0.330535	−	0.126880i	−0.0212476	−	0.00815619i
$243$	5.76116	−	21.5009i	0.369579	−	1.37929i
$244$	−6.12380	−	4.44920i	−0.392036	−	0.284831i
$245$		0			0
$246$	−0.325245	+	0.236304i	−0.0207368	+	0.0150662i
$247$	10.2817	+	26.7848i	0.654211	+	1.70428i
$248$	0.709111	+	1.09193i	0.0450286	+	0.0693379i
$249$	13.4758	+	7.78025i	0.853994	+	0.493054i
$250$		0			0
$251$		−	23.2521i		−	1.46766i	−0.679334	−	0.733829i	$-0.737731\pi$
$251$		−	23.2521i		−	1.46766i	0.679334	−	0.733829i	$-0.262269\pi$
$252$	−0.0119562	+	18.1333i	−0.000753172	+	1.14229i
$253$	−3.51481	+	22.1916i	−0.220974	+	1.39517i
$254$	−1.05356	+	2.36632i	−0.0661059	+	0.148476i
$255$		0			0
$256$	9.80414	−	4.36508i	0.612759	−	0.272818i
$257$	−0.313748	−	0.0840686i	−0.0195711	−	0.00524406i	0.249020	−	0.968498i	$-0.419891\pi$
$257$	−0.313748	−	0.0840686i	−0.0195711	−	0.00524406i	−0.268591	+	0.963254i	$0.586558\pi$
$258$	−0.843105	−	5.32315i	−0.0524894	−	0.331405i
$259$	−8.18727	−	10.1241i	−0.508732	−	0.629080i
$260$		0			0
$261$	−0.595620	+	0.661503i	−0.0368679	+	0.0409460i
$262$	3.57742	+	0.187485i	0.221014	+	0.0115828i
$263$	6.74598	+	0.353542i	0.415975	+	0.0218003i	0.259176	−	0.965830i	$-0.416549\pi$
$263$	6.74598	+	0.353542i	0.415975	+	0.0218003i	0.156799	+	0.987631i	$0.449882\pi$
$264$	−6.23037	+	6.91953i	−0.383453	+	0.425867i
$265$		0			0
$266$	−1.95587	+	5.08519i	−0.119922	+	0.311793i
$267$	−1.54003	−	9.72338i	−0.0942484	−	0.595061i
$268$	2.21104	+	0.592447i	0.135061	+	0.0361895i
$269$	0.532457	−	0.237065i	0.0324645	−	0.0144541i	−0.390440	−	0.920628i	$-0.627677\pi$
$269$	0.532457	−	0.237065i	0.0324645	−	0.0144541i	0.422905	+	0.906174i	$0.361011\pi$
$270$		0			0
$271$	7.55674	−	16.9727i	0.459039	−	1.03102i	−0.524679	−	0.851300i	$-0.675815\pi$
$271$	7.55674	−	16.9727i	0.459039	−	1.03102i	0.983718	−	0.179719i	$-0.0575187\pi$
$272$	3.30935	−	20.8944i	0.200659	−	1.26691i
$273$	−12.4409	+	21.5156i	−0.752960	+	1.30218i
$274$		−	1.60679i		−	0.0970698i
$275$		0			0
$276$	27.3645	+	15.7989i	1.64715	+	0.950981i
$277$	−0.818099	−	1.25976i	−0.0491548	−	0.0756917i	0.813239	−	0.581930i	$-0.197702\pi$
$277$	−0.818099	−	1.25976i	−0.0491548	−	0.0756917i	−0.862394	+	0.506238i	$0.831036\pi$
$278$	0.0403718	+	0.105172i	0.00242134	+	0.00630781i
$279$	3.61115	−	2.62366i	0.216194	−	0.157074i
$280$		0			0
$281$	24.2076	+	17.5878i	1.44410	+	1.04920i	0.987165	+	0.159702i	$0.0510533\pi$
$281$	24.2076	+	17.5878i	1.44410	+	1.04920i	0.456936	+	0.889499i	$0.348947\pi$
$282$	−0.183231	+	0.683827i	−0.0109112	+	0.0407213i
$283$	−8.38668	−	3.21935i	−0.498537	−	0.191370i	0.0960894	−	0.995373i	$-0.469367\pi$
$283$	−8.38668	−	3.21935i	−0.498537	−	0.191370i	−0.594626	+	0.804002i	$0.702700\pi$
$284$	−12.6533	+	11.3931i	−0.750836	+	0.676056i
$285$		0			0
$286$	−3.23105	+	1.04983i	−0.191056	+	0.0620779i
$287$	1.27565	+	0.928102i	0.0752994	+	0.0547841i
$288$	4.86148	+	9.54119i	0.286465	+	0.562220i
$289$	−13.1949	−	11.8807i	−0.776170	−	0.698867i
$290$		0			0
$291$	17.4508	+	19.3811i	1.02299	+	1.13614i
$292$	−9.74014	−	12.0281i	−0.569998	−	0.703889i
$293$	−19.5938	−	19.5938i	−1.14468	−	1.14468i	−0.987583	−	0.157096i	$-0.949787\pi$
$293$	−19.5938	−	19.5938i	−1.14468	−	1.14468i	−0.157096	−	0.987583i	$-0.550213\pi$
$294$	−4.49064	+	1.45255i	−0.261900	+	0.0847146i
$295$		0			0
$296$	−4.65539	−	2.07271i	−0.270589	−	0.120474i
$297$	3.84386	+	3.11270i	0.223043	+	0.180617i
$298$	−0.710179	+	0.461195i	−0.0411395	+	0.0267163i
$299$	11.7362	+	20.3277i	0.678723	+	1.17558i
$300$		0			0
$301$	−18.8498	+	9.58879i	−1.08648	+	0.552689i
$302$	−0.655084	+	1.28567i	−0.0376959	+	0.0739823i
$303$	25.8983	−	9.94141i	1.48782	−	0.571119i
$304$	−2.93194	−	27.8955i	−0.168158	−	1.59992i
$305$		0			0
$306$	5.48350	+	0.576339i	0.313471	+	0.0329471i
$307$	−4.81162	+	4.81162i	−0.274613	+	0.274613i	−0.830954	−	0.556341i	$-0.812205\pi$
$307$	−4.81162	+	4.81162i	−0.274613	+	0.274613i	0.556341	+	0.830954i	$0.312205\pi$
$308$	16.3896	+	7.31009i	0.933886	+	0.416531i
$309$	−12.0008	−	3.89928i	−0.682699	−	0.221822i
$310$		0			0
$311$	6.33562	−	29.8067i	0.359260	−	1.69018i	−0.312906	−	0.949784i	$-0.601303\pi$
$311$	6.33562	−	29.8067i	0.359260	−	1.69018i	0.672166	−	0.740401i	$-0.265364\pi$
$312$	−0.509088	+	9.71397i	−0.0288214	+	0.549946i
$313$	10.4215	+	6.76777i	0.589055	+	0.382537i	0.804477	−	0.593984i	$-0.202446\pi$
$313$	10.4215	+	6.76777i	0.589055	+	0.382537i	−0.215421	+	0.976521i	$0.569112\pi$
$314$	−1.64929	−	5.07598i	−0.0930747	−	0.286454i
$315$		0			0
$316$	−5.87245	+	18.0735i	−0.330351	+	1.01672i
$317$	−2.13910	+	1.73221i	−0.120144	+	0.0972906i	−0.687509	−	0.726175i	$-0.741296\pi$
$317$	−2.13910	+	1.73221i	−0.120144	+	0.0972906i	0.567366	+	0.823466i	$0.307963\pi$
$318$	1.92866	−	0.516782i	0.108154	−	0.0289797i
$319$	0.358312	+	0.804782i	0.0200616	+	0.0450591i
$320$		0			0
$321$	12.9773	+	17.8618i	0.724325	+	0.996948i
$322$	−0.929631	+	4.35944i	−0.0518063	+	0.242942i
$323$	−41.0595	−	20.9209i	−2.28461	−	1.16407i
$324$	−11.7826	+	6.80267i	−0.654587	+	0.377926i
$325$		0			0
$326$	1.14676	−	1.98624i	0.0635130	−	0.110008i
$327$	−1.16663	−	22.2607i	−0.0645150	−	1.23102i
$328$	0.609829	+	0.0965874i	0.0336722	+	0.00533315i
$329$	2.77430	−	0.143560i	0.152952	−	0.00791475i
$330$		0			0
$331$	−2.12996	+	20.2652i	−0.117073	+	1.11388i	0.765413	+	0.643540i	$0.222535\pi$
$331$	−2.12996	+	20.2652i	−0.117073	+	1.11388i	−0.882486	+	0.470339i	$0.844132\pi$
$332$	−3.03800	−	11.3380i	−0.166732	−	0.622253i
$333$	−6.26092	+	16.3103i	−0.343096	+	0.893796i
$334$	−5.04018	+	1.07132i	−0.275786	+	0.0586202i
$335$		0			0
$336$	17.1926	−	17.1700i	0.937935	−	0.936699i
$337$	−12.2954	+	6.26481i	−0.669772	+	0.341266i	−0.755590	−	0.655045i	$-0.772650\pi$
$337$	−12.2954	+	6.26481i	−0.669772	+	0.341266i	0.0858177	+	0.996311i	$0.472650\pi$
$338$	−0.0677239	+	0.104286i	−0.00368369	+	0.00567239i
$339$	19.8166	+	4.21215i	1.07629	+	0.228772i
$340$		0			0
$341$	−0.918453	−	4.32098i	−0.0497370	−	0.233994i
$342$	7.22059	−	1.14363i	0.390445	−	0.0618404i
$343$	10.8563	+	15.0047i	0.586184	+	0.810178i
$344$	−4.86523	+	6.69641i	−0.262315	+	0.361046i
$345$		0			0
$346$	−2.20029	+	0.231260i	−0.118288	+	0.0124326i
$347$	1.58176	−	1.95331i	0.0849134	−	0.104859i	−0.732919	−	0.680316i	$-0.761842\pi$
$347$	1.58176	−	1.95331i	0.0849134	−	0.104859i	0.817832	+	0.575457i	$0.195176\pi$
$348$	1.23720	−	0.0648389i	0.0663209	−	0.00347573i
$349$	−27.7478			−1.48531			−0.742654	−	0.669676i	$-0.766433\pi$
$349$	−27.7478			−1.48531			−0.742654	+	0.669676i	$0.766433\pi$
$350$		0			0
$351$	5.16719			0.275804
$352$	10.5832	−	0.554640i	0.564085	−	0.0295624i
$353$	−15.3616	+	18.9700i	−0.817614	+	1.00967i	0.182038	+	0.983291i	$0.441731\pi$
$353$	−15.3616	+	18.9700i	−0.817614	+	1.00967i	−0.999652	+	0.0263777i	$0.991603\pi$
$354$	3.74463	−	0.393577i	0.199025	−	0.0209184i
$355$		0			0
$356$	−4.36500	+	6.00791i	−0.231345	+	0.318418i
$357$	−8.27395	−	39.0525i	−0.437904	−	2.06688i
$358$	−3.99889	+	0.633362i	−0.211348	+	0.0334742i
$359$	7.52675	+	35.4106i	0.397247	+	1.86890i	0.487719	+	0.873000i	$0.337829\pi$
$359$	7.52675	+	35.4106i	0.397247	+	1.86890i	−0.0904726	+	0.995899i	$0.528838\pi$
$360$		0			0
$361$	−41.1801	−	8.75310i	−2.16737	−	0.460690i
$362$	1.10991	−	1.70911i	0.0583355	−	0.0898287i
$363$	3.06460	−	1.56149i	0.160850	−	0.0819571i
$364$	18.1124	−	4.84041i	0.949349	−	0.253707i
$365$		0			0
$366$	−2.58580	+	0.549628i	−0.135162	+	0.0287295i
$367$	−4.23406	+	11.0301i	−0.221016	+	0.575766i	−0.998593	−	0.0530209i	$-0.983115\pi$
$367$	−4.23406	+	11.0301i	−0.221016	+	0.575766i	0.777577	+	0.628787i	$0.216448\pi$
$368$	−5.93934	−	22.1659i	−0.309609	−	1.15548i
$369$	0.221261	−	2.10516i	0.0115184	−	0.109590i
$370$		0			0
$371$	−4.26294	−	6.57384i	−0.221321	−	0.341297i
$372$	−6.13600	−	0.971847i	−0.318137	−	0.0503879i
$373$	1.03759	+	19.7985i	0.0537246	+	1.02513i	0.883916	+	0.467647i	$0.154898\pi$
$373$	1.03759	+	19.7985i	0.0537246	+	1.02513i	−0.830191	+	0.557479i	$0.811769\pi$
$374$	2.72837	−	4.72568i	0.141081	−	0.244359i
$375$		0			0
$376$	0.941605	−	0.543636i	0.0485596	−	0.0280359i
$377$	0.820009	+	0.417815i	0.0422326	+	0.0215186i
$378$	0.728784	+	0.657070i	0.0374846	+	0.0337961i
$379$	8.72393	+	12.0075i	0.448118	+	0.616782i	0.971992	−	0.235014i	$-0.0755136\pi$
$379$	8.72393	+	12.0075i	0.448118	+	0.616782i	−0.523874	+	0.851796i	$0.675514\pi$
$380$		0			0
$381$	−10.2349	−	22.9880i	−0.524351	−	1.17771i
$382$	−1.75881	+	0.471271i	−0.0899884	+	0.0241123i
$383$	22.0440	−	17.8508i	1.12639	−	0.912135i	0.129553	−	0.991572i	$-0.458646\pi$
$383$	22.0440	−	17.8508i	1.12639	−	0.912135i	0.996840	+	0.0794371i	$0.0253123\pi$
$384$	6.10085	−	18.7765i	0.311333	−	0.958184i
$385$		0			0
$386$	0.804035	+	2.47457i	0.0409243	+	0.125952i
$387$	23.7990	+	15.4553i	1.20977	+	0.785635i
$388$	1.02961	−	19.6462i	0.0522706	−	0.997383i
$389$	4.29281	−	20.1961i	0.217654	−	1.02398i	−0.724622	−	0.689146i	$-0.757986\pi$
$389$	4.29281	−	20.1961i	0.217654	−	1.02398i	0.942276	−	0.334836i	$-0.108681\pi$
$390$		0			0
$391$	−35.8559	−	11.6503i	−1.81331	−	0.589180i
$392$	6.45417	+	3.29929i	0.325985	+	0.166639i
$393$	−24.6081	+	24.6081i	−1.24131	+	1.24131i
$394$	1.55396	+	0.163328i	0.0782875	+	0.00822835i
$395$		0			0
$396$	−2.51703	−	23.9480i	−0.126486	−	1.20343i
$397$	−0.983037	+	0.377352i	−0.0493372	+	0.0189388i	−0.382911	−	0.923785i	$-0.625079\pi$
$397$	−0.983037	+	0.377352i	−0.0493372	+	0.0189388i	0.333574	+	0.942724i	$0.391745\pi$
$398$	0.169973	−	0.333590i	0.00851996	−	0.0167214i
$399$	−23.9981	−	47.1758i	−1.20141	−	2.36175i
$400$		0			0
$401$	0.184864	+	0.320194i	0.00923166	+	0.0159897i	0.870604	−	0.491984i	$-0.163728\pi$
$401$	0.184864	+	0.320194i	0.00923166	+	0.0159897i	−0.861373	+	0.507974i	$0.830395\pi$
$402$	0.670459	−	0.435401i	0.0334395	−	0.0217158i
$403$	−3.58649	−	2.90429i	−0.178656	−	0.144673i
$404$	−19.1169	−	8.51139i	−0.951101	−	0.423458i
$405$		0			0
$406$	0.0625242	+	0.163203i	0.00310303	+	0.00809962i
$407$	12.2260	+	12.2260i	0.606019	+	0.606019i
$408$	−9.83241	−	12.1420i	−0.486777	−	0.601119i
$409$	−19.6346	−	21.8064i	−0.970868	−	1.07826i	−0.996906	−	0.0785970i	$-0.974956\pi$
$409$	−19.6346	−	21.8064i	−0.970868	−	1.07826i	0.0260387	−	0.999661i	$-0.491711\pi$
$410$		0			0
$411$	11.6001	+	10.4447i	0.572189	+	0.515201i
$412$	4.32133	+	8.48108i	0.212897	+	0.417833i
$413$	−6.00060	−	13.5015i	−0.295270	−	0.664367i
$414$	5.68828	−	1.84823i	0.279564	−	0.0908357i
$415$		0			0
$416$	8.22762	−	7.40818i	0.403392	−	0.363216i
$417$	−1.02171	−	0.392198i	−0.0500334	−	0.0192060i
$418$	1.87257	−	6.98854i	0.0915906	−	0.341821i
$419$	6.95129	+	5.05041i	0.339593	+	0.246729i	0.744490	−	0.667634i	$-0.232693\pi$
$419$	6.95129	+	5.05041i	0.339593	+	0.246729i	−0.404897	+	0.914362i	$0.632693\pi$
$420$		0			0
$421$	25.8891	−	18.8095i	1.26176	−	0.916720i	0.262914	−	0.964819i	$-0.415317\pi$
$421$	25.8891	−	18.8095i	1.26176	−	0.916720i	0.998843	+	0.0480998i	$0.0153165\pi$
$422$	−1.26845	−	3.30442i	−0.0617471	−	0.160857i
$423$	−2.03016	−	3.12617i	−0.0987097	−	0.152000i
$424$	−2.65569	−	1.53326i	−0.128972	−	0.0744619i
$425$		0			0
$426$			5.94645i			0.288107i
$427$	5.18077	+	8.98704i	0.250715	+	0.434914i
$428$	2.60536	−	16.4496i	0.125935	−	0.795122i
$429$	13.4239	−	30.1506i	0.648112	−	1.45568i
$430$		0			0
$431$	28.5735	−	12.7218i	1.37634	−	0.612785i	0.420666	−	0.907216i	$-0.361797\pi$
$431$	28.5735	−	12.7218i	1.37634	−	0.612785i	0.955673	+	0.294430i	$0.0951299\pi$
$432$	−4.87957	−	1.30748i	−0.234769	−	0.0629060i
$433$	0.266365	+	1.68176i	0.0128007	+	0.0808204i	0.993262	−	0.115893i	$-0.0369731\pi$
$433$	0.266365	+	1.68176i	0.0128007	+	0.0808204i	−0.980461	+	0.196714i	$0.936973\pi$
$434$	−0.136526	−	0.865688i	−0.00655348	−	0.0415543i
$435$		0			0
$436$	−11.2516	+	12.4962i	−0.538853	+	0.598457i
$437$	−49.9192	−	2.61616i	−2.38796	−	0.125148i
$438$	−5.39790	−	0.282892i	−0.257922	−	0.0135171i
$439$	−19.8967	+	22.0975i	−0.949616	+	1.05466i	0.0488236	+	0.998807i	$0.484453\pi$
$439$	−19.8967	+	22.0975i	−0.949616	+	1.05466i	−0.998439	+	0.0558477i	$0.982214\pi$
$440$		0			0
$441$	10.1375	−	22.6887i	0.482739	−	1.08041i
$442$	−0.891775	−	5.63045i	−0.0424174	−	0.267813i
$443$	24.2744	+	6.50431i	1.15331	+	0.309029i	0.784292	−	0.620392i	$-0.213026\pi$
$443$	24.2744	+	6.50431i	1.15331	+	0.309029i	0.369021	+	0.929421i	$0.379693\pi$
$444$	22.2135	−	9.89008i	1.05421	−	0.469362i
$445$		0			0
$446$	2.22114	−	4.98876i	0.105174	−	0.236224i
$447$	1.28687	−	8.12500i	0.0608671	−	0.384299i
$448$	−16.8855	−	0.0111335i	−0.797764	−	0.000526008i
$449$		−	19.5516i		−	0.922696i	−0.887219	−	0.461348i	$-0.847366\pi$
$449$		−	19.5516i		−	0.922696i	0.887219	−	0.461348i	$-0.152634\pi$
$450$		0			0
$451$	−1.81423	−	1.04744i	−0.0854285	−	0.0493222i
$452$	−8.32341	−	12.8169i	−0.391500	−	0.602858i
$453$	−5.02351	−	13.0867i	−0.236025	−	0.614866i
$454$	−3.13294	+	2.27621i	−0.147036	+	0.106828i
$455$		0			0
$456$	−16.7593	−	12.1763i	−0.784825	−	0.570209i
$457$	1.63299	−	6.09440i	0.0763880	−	0.285084i	−0.917156	−	0.398527i	$-0.869521\pi$
$457$	1.63299	−	6.09440i	0.0763880	−	0.285084i	0.993544	+	0.113443i	$0.0361881\pi$
$458$	−4.92089	−	1.88895i	−0.229938	−	0.0882650i
$459$	−6.16771	+	5.55343i	−0.287884	+	0.259212i
$460$		0			0
$461$	5.06458	−	1.64558i	0.235881	−	0.0766424i	−0.188691	−	0.982036i	$-0.560425\pi$
$461$	5.06458	−	1.64558i	0.235881	−	0.0766424i	0.424572	+	0.905394i	$0.360425\pi$
$462$	5.72732	−	2.54544i	0.266459	−	0.118425i
$463$	10.0937	+	19.8100i	0.469094	+	0.920649i	0.997432	+	0.0716148i	$0.0228152\pi$
$463$	10.0937	+	19.8100i	0.469094	+	0.920649i	−0.528338	+	0.849034i	$0.677185\pi$
$464$	−0.668643	−	0.602049i	−0.0310410	−	0.0279494i
$465$		0			0
$466$	1.20458	+	1.33782i	0.0558009	+	0.0619732i
$467$	−4.68313	−	5.78319i	−0.216709	−	0.267614i	0.657185	−	0.753729i	$-0.271747\pi$
$467$	−4.68313	−	5.78319i	−0.216709	−	0.267614i	−0.873895	+	0.486115i	$0.838414\pi$
$468$	−17.7881	−	17.7881i	−0.822254	−	0.822254i
$469$	−2.43659	−	1.97577i	−0.112511	−	0.0912326i
$470$		0			0
$471$	47.3665	+	21.0889i	2.18253	+	0.971727i
$472$	−4.49400	−	3.63917i	−0.206853	−	0.167506i
$473$	23.5531	−	15.2956i	1.08297	−	0.703291i
$474$	3.31844	+	5.74771i	0.152421	+	0.264001i
$475$		0			0
$476$	−16.4173	+	25.2439i	−0.752485	+	1.15705i
$477$	−4.77284	+	9.36722i	−0.218533	+	0.428895i
$478$	1.05283	−	0.404142i	0.0481552	−	0.0184850i
$479$	1.32701	+	12.6257i	0.0606327	+	0.576881i	0.982091	+	0.188405i	$0.0603318\pi$
$479$	1.32701	+	12.6257i	0.0606327	+	0.576881i	−0.921459	+	0.388476i	$0.873002\pi$
$480$		0			0
$481$	17.9640	+	1.88809i	0.819087	+	0.0860895i
$482$	0.681684	−	0.681684i	0.0310498	−	0.0310498i
$483$	−25.4295	−	35.0493i	−1.15708	−	1.59480i
$484$	−2.46756	−	0.801759i	−0.112162	−	0.0364436i
$485$		0			0
$486$	−1.21924	+	5.73606i	−0.0553057	+	0.260193i
$487$	0.821060	−	15.6668i	0.0372058	−	0.709928i	−0.914811	−	0.403882i	$-0.867661\pi$
$487$	0.821060	−	15.6668i	0.0372058	−	0.709928i	0.952017	−	0.306046i	$-0.0990062\pi$
$488$	3.40500	+	2.21123i	0.154137	+	0.100098i
$489$	6.88511	+	21.1902i	0.311355	+	0.958254i
$490$		0			0
$491$	4.43552	−	13.6511i	0.200172	−	0.616067i	−0.799705	−	0.600393i	$-0.795011\pi$
$491$	4.43552	−	13.6511i	0.200172	−	0.616067i	0.999877	−	0.0156736i	$-0.00498927\pi$
$492$	−2.28955	+	1.85404i	−0.103221	+	0.0835868i
$493$	−1.42783	+	0.382586i	−0.0643063	+	0.0172308i
$494$	−3.07430	−	6.90498i	−0.138319	−	0.310670i
$495$		0			0
$496$	2.65198	+	3.65013i	0.119077	+	0.163896i
$497$	22.1967	−	7.19596i	0.995657	−	0.322783i
$498$	−3.65258	−	1.86108i	−0.163676	−	0.0833972i
$499$	6.68368	−	3.85883i	0.299203	−	0.172745i	−0.342882	−	0.939378i	$-0.611403\pi$
$499$	6.68368	−	3.85883i	0.299203	−	0.172745i	0.642085	+	0.766634i	$0.278070\pi$
$500$		0			0
$501$	25.0287	−	43.3511i	1.11820	−	1.93678i
$502$	0.320595	+	6.11732i	0.0143089	+	0.273030i
$503$	9.64392	+	1.52745i	0.430001	+	0.0681055i	0.367684	−	0.929951i	$-0.380151\pi$
$503$	9.64392	+	1.52745i	0.430001	+	0.0681055i	0.0623173	+	0.998056i	$0.480151\pi$
$504$	−0.502621	−	9.71312i	−0.0223885	−	0.432657i
$505$		0			0
$506$	0.618727	−	5.88679i	0.0275058	−	0.261700i
$507$	−0.312649	−	1.16682i	−0.0138852	−	0.0518203i
$508$	−6.80251	+	17.7211i	−0.301812	+	0.786248i
$509$	5.47118	−	1.16293i	0.242506	−	0.0515462i	−0.0850552	−	0.996376i	$-0.527107\pi$
$509$	5.47118	−	1.16293i	0.242506	−	0.0515462i	0.327561	+	0.944830i	$0.393773\pi$
$510$		0			0
$511$	5.47617	+	20.4914i	0.242252	+	0.906486i
$512$	−16.2658	+	8.28783i	−0.718853	+	0.366274i
$513$	−5.99333	+	9.22892i	−0.264612	+	0.407467i
$514$	0.0837023	+	0.0177915i	0.00369195	+	0.000784748i
$515$		0			0
$516$	−8.21152	−	38.6322i	−0.361492	−	1.70069i
$517$	−3.64360	+	0.577090i	−0.160245	+	0.0253804i
$518$	2.29356	+	2.55063i	0.100773	+	0.112068i
$519$	12.6331	−	17.3880i	0.554534	−	0.763250i
$520$		0			0
$521$	−35.0701	+	3.68601i	−1.53645	+	0.161487i	−0.834606	−	0.550847i	$-0.814305\pi$
$521$	−35.0701	+	3.68601i	−1.53645	+	0.161487i	−0.701841	+	0.712334i	$0.747638\pi$
$522$	0.147579	−	0.182245i	0.00645937	−	0.00797666i
$523$	−17.6409	+	0.924518i	−0.771381	+	0.0404264i	−0.433965	−	0.900930i	$-0.642886\pi$
$523$	−17.6409	+	0.924518i	−0.771381	+	0.0404264i	−0.337415	+	0.941356i	$0.609553\pi$
$524$	26.2519			1.14682
$525$		0			0
$526$	−1.77966			−0.0775967
$527$	7.40232	−	0.387939i	0.322450	−	0.0168989i
$528$	−20.3058	+	25.0756i	−0.883697	+	1.09127i
$529$	−17.7983	+	1.87068i	−0.773841	+	0.0813340i
$530$		0			0
$531$	−11.6528	+	16.0388i	−0.505690	+	0.696023i
$532$	−12.3630	+	37.9642i	−0.536004	+	1.64596i
$533$	−2.16157	+	0.342360i	−0.0936282	+	0.0148292i
$534$	0.539227	+	2.53686i	0.0233346	+	0.109781i
$535$		0			0
$536$	−1.20094	−	0.255267i	−0.0518726	−	0.0110259i
$537$	21.4218	−	32.9867i	0.924418	−	1.42348i
$538$	−0.136814	+	0.0697102i	−0.00589847	+	0.00300542i
$539$	−16.4323	−	18.2984i	−0.707789	−	0.788167i
$540$		0			0
$541$	14.5992	−	3.10316i	0.627669	−	0.133415i	0.116915	−	0.993142i	$-0.462700\pi$
$541$	14.5992	−	3.10316i	0.627669	−	0.133415i	0.510754	+	0.859727i	$0.329366\pi$
$542$	−1.75406	+	4.56950i	−0.0753435	+	0.196277i
$543$	5.12391	+	19.1227i	0.219888	+	0.820634i
$544$	−1.85879	+	17.6852i	−0.0796951	+	0.758248i
$545$		0			0
$546$	2.97640	−	5.83201i	0.127378	−	0.249587i
$547$	−43.4146	−	6.87620i	−1.85627	−	0.294005i	−0.874639	−	0.484774i	$-0.838902\pi$
$547$	−43.4146	−	6.87620i	−1.85627	−	0.294005i	−0.981635	+	0.190769i	$0.938902\pi$
$548$	−0.616248	−	11.7587i	−0.0263248	−	0.502307i
$549$	6.95951	−	12.0542i	0.297025	−	0.514462i
$550$		0			0
$551$	−1.69736	+	0.979969i	−0.0723098	+	0.0417481i
$552$	−15.1008	−	7.69424i	−0.642733	−	0.327489i
$553$	17.4391	−	19.3424i	0.741585	−	0.822522i
$554$	0.232601	+	0.320147i	0.00988226	+	0.0136018i
$555$		0			0
$556$	0.335782	+	0.754180i	0.0142403	+	0.0319843i
$557$	2.55339	−	0.684178i	0.108190	−	0.0289895i	−0.204318	−	0.978905i	$-0.565498\pi$
$557$	2.55339	−	0.684178i	0.108190	−	0.0289895i	0.312508	+	0.949915i	$0.398831\pi$
$558$	−0.913874	+	0.740040i	−0.0386874	+	0.0313284i
$559$	9.06628	−	27.9031i	0.383463	−	1.18018i
$560$		0			0
$561$	16.3811	+	50.4159i	0.691611	+	2.12856i
$562$	−6.61120	−	4.29336i	−0.278877	−	0.181105i
$563$	1.56885	−	29.9354i	0.0661191	−	1.26163i	−0.741108	−	0.671386i	$-0.765699\pi$
$563$	1.56885	−	29.9354i	0.0661191	−	1.26163i	0.807227	−	0.590241i	$-0.200967\pi$
$564$	−1.07864	+	5.07461i	−0.0454190	+	0.213680i
$565$		0			0
$566$	2.25082	+	0.731335i	0.0946089	+	0.0307403i
$567$	18.5443	−	1.93673i	0.778789	−	0.0813349i
$568$	6.45771	−	6.45771i	0.270959	−	0.270959i
$569$	−32.8105	−	3.44853i	−1.37549	−	0.144570i	−0.612239	−	0.790673i	$-0.709731\pi$
$569$	−32.8105	−	3.44853i	−1.37549	−	0.144570i	−0.763250	+	0.646103i	$0.776398\pi$
$570$		0			0
$571$	3.39211	+	32.2738i	0.141956	+	1.35062i	0.801068	+	0.598573i	$0.204265\pi$
$571$	3.39211	+	32.2738i	0.141956	+	1.35062i	−0.659113	+	0.752044i	$0.729068\pi$
$572$	−23.2426	+	8.92201i	−0.971823	+	0.373048i
$573$	8.03061	−	15.7610i	0.335484	−	0.658424i
$574$	−0.348405	−	0.226583i	−0.0145421	−	0.00945741i
$575$		0			0
$576$	11.3285	+	19.6215i	0.472020	+	0.817562i
$577$	0.111322	−	0.0722936i	0.00463441	−	0.00300962i	−0.542320	−	0.840172i	$-0.682454\pi$
$577$	0.111322	−	0.0722936i	0.00463441	−	0.00300962i	0.546954	+	0.837163i	$0.315787\pi$
$578$	3.63522	+	2.94374i	0.151205	+	0.122443i
$579$	−23.0914	−	10.2810i	−0.959646	−	0.427262i
$580$		0			0
$581$	−2.52689	+	15.8864i	−0.104833	+	0.659077i
$582$	−4.85831	−	4.85831i	−0.201384	−	0.201384i
$583$	6.54774	+	8.08578i	0.271180	+	0.334879i
$584$	5.55478	+	6.16921i	0.229858	+	0.255284i
$585$		0			0
$586$	5.42502	+	4.88471i	0.224106	+	0.201786i
$587$	12.7376	+	24.9989i	0.525736	+	1.03182i	0.989320	+	0.145762i	$0.0465634\pi$
$587$	12.7376	+	24.9989i	0.525736	+	1.03182i	−0.463584	+	0.886053i	$0.653437\pi$
$588$	−32.3060	+	12.3523i	−1.33228	+	0.509399i
$589$	9.34714	−	3.03707i	0.385142	−	0.125140i
$590$		0			0
$591$	−11.2805	+	10.1570i	−0.464017	+	0.417802i
$592$	−16.4863	−	6.32850i	−0.677583	−	0.260100i
$593$	−11.6217	+	43.3728i	−0.477247	+	1.78111i	0.135442	+	0.990785i	$0.456754\pi$
$593$	−11.6217	+	43.3728i	−0.477247	+	1.78111i	−0.612689	+	0.790324i	$0.709912\pi$
$594$	−1.05419	−	0.765913i	−0.0432539	−	0.0314258i
$595$		0			0
$596$	−5.02030	+	3.64746i	−0.205639	+	0.149406i
$597$	1.30343	+	3.39556i	0.0533460	+	0.138971i
$598$	−3.36793	−	5.18615i	−0.137725	−	0.212078i
$599$	18.7555	+	10.8285i	0.766331	+	0.442441i	0.831564	−	0.555429i	$-0.187446\pi$
$599$	18.7555	+	10.8285i	0.766331	+	0.442441i	−0.0652335	+	0.997870i	$0.520779\pi$
$600$		0			0
$601$		−	27.1300i		−	1.10666i	−0.832963	−	0.553328i	$-0.813357\pi$
$601$		−	27.1300i		−	1.10666i	0.832963	−	0.553328i	$-0.186643\pi$
$602$	4.82693	−	2.78259i	0.196731	−	0.113410i
$603$	−0.658463	+	4.15737i	−0.0268147	+	0.169301i
$604$	−4.30090	+	9.65998i	−0.175001	+	0.393059i
$605$		0			0
$606$	−6.67644	+	2.97254i	−0.271212	+	0.120751i
$607$	−3.36494	−	0.901633i	−0.136579	−	0.0365961i	0.189882	−	0.981807i	$-0.439189\pi$
$607$	−3.36494	−	0.901633i	−0.136579	−	0.0365961i	−0.326461	+	0.945211i	$0.605856\pi$
$608$	3.68840	+	23.2877i	0.149584	+	0.944439i
$609$	−1.58466	−	0.609492i	−0.0642135	−	0.0246979i
$610$		0			0
$611$	−2.57876	+	2.86401i	−0.104326	+	0.115865i
$612$	40.3500	+	2.11466i	1.63105	+	0.0854799i
$613$	−32.9083	−	1.72465i	−1.32916	−	0.0696581i	−0.625514	−	0.780213i	$-0.715111\pi$
$613$	−32.9083	−	1.72465i	−1.32916	−	0.0696581i	−0.703642	+	0.710555i	$0.748444\pi$
$614$	1.19953	−	1.33222i	0.0484092	−	0.0537639i
$615$		0			0
$616$	−8.98402	−	3.45544i	−0.361977	−	0.139224i
$617$	−6.30591	−	39.8140i	−0.253866	−	1.60285i	−0.704208	−	0.709994i	$-0.748698\pi$
$617$	−6.30591	−	39.8140i	−0.253866	−	1.60285i	0.450342	−	0.892856i	$-0.351302\pi$
$618$	3.21101	+	0.860387i	0.129166	+	0.0346098i
$619$	−26.1694	+	11.6513i	−1.05184	+	0.468307i	−0.858494	−	0.512824i	$-0.828599\pi$
$619$	−26.1694	+	11.6513i	−1.05184	+	0.468307i	−0.193342	+	0.981131i	$0.561933\pi$
$620$		0			0
$621$	−3.66180	+	8.22453i	−0.146943	+	0.330039i
$622$	−1.25585	+	7.92913i	−0.0503550	+	0.317929i
$623$	8.81697	−	5.08273i	0.353244	−	0.203635i
$624$			33.7084i			1.34942i
$625$		0			0
$626$	−2.83506	−	1.63683i	−0.113312	−	0.0654207i
$627$	38.2806	+	58.9470i	1.52878	+	2.35412i
$628$	−14.0165	−	36.5142i	−0.559318	−	1.45707i
$629$	−23.4715	+	17.0531i	−0.935872	+	0.679951i
$630$		0			0
$631$	−34.7400	−	25.2401i	−1.38298	−	1.00479i	−0.996595	−	0.0824526i	$-0.973725\pi$
$631$	−34.7400	−	25.2401i	−1.38298	−	1.00479i	−0.386382	−	0.922339i	$-0.626275\pi$
$632$	2.63813	−	9.84562i	0.104939	−	0.391638i
$633$	32.1013	+	12.3225i	1.27591	+	0.489777i
$634$	0.538887	−	0.485216i	0.0214019	−	0.0192704i
$635$		0			0
$636$	13.9160	−	4.52157i	0.551804	−	0.179292i
$637$	−25.3713	−	4.05272i	−1.00525	−	0.160575i
$638$	−0.105363	−	0.206787i	−0.00417138	−	0.00818680i
$639$	−23.2675	−	20.9502i	−0.920448	−	0.828775i
$640$		0			0
$641$	20.7202	+	23.0121i	0.818399	+	0.908924i	0.997186	−	0.0749634i	$-0.0238840\pi$
$641$	20.7202	+	23.0121i	0.818399	+	0.908924i	−0.178787	+	0.983888i	$0.557217\pi$
$642$	−3.66045	−	4.52028i	−0.144466	−	0.178401i
$643$	10.0822	+	10.0822i	0.397604	+	0.397604i	0.877387	−	0.479783i	$-0.159285\pi$
$643$	10.0822	+	10.0822i	0.397604	+	0.397604i	−0.479783	+	0.877387i	$0.659285\pi$
$644$	−5.13120	+	32.2595i	−0.202198	+	1.27120i
$645$		0			0
$646$	11.0907	+	4.93789i	0.436357	+	0.194279i
$647$	−22.0741	−	17.8753i	−0.867823	−	0.702749i	0.0881806	−	0.996105i	$-0.471895\pi$
$647$	−22.0741	−	17.8753i	−0.867823	−	0.702749i	−0.956003	+	0.293355i	$0.905228\pi$
$648$	6.12017	−	3.97448i	0.240423	−	0.156132i
$649$	9.81009	+	16.9916i	0.385080	+	0.666977i
$650$		0			0
$651$	7.13722	+	4.64166i	0.279730	+	0.181921i
$652$	7.63034	−	14.9754i	0.298827	−	0.586481i
$653$	31.5132	−	12.0968i	1.23321	−	0.473383i	0.347521	−	0.937672i	$-0.387023\pi$
$653$	31.5132	−	12.0968i	1.23321	−	0.473383i	0.885684	+	0.464289i	$0.153690\pi$
$654$	0.613853	+	5.84042i	0.0240036	+	0.228379i
$655$		0			0
$656$	2.12788	+	0.223650i	0.0830799	+	0.00873205i
$657$	20.1244	−	20.1244i	0.785129	−	0.785129i
$658$	−0.727903	+	0.0760204i	−0.0283766	+	0.00296359i
$659$	1.81381	+	0.589344i	0.0706562	+	0.0229576i	0.344132	−	0.938921i	$-0.388173\pi$
$659$	1.81381	+	0.589344i	0.0706562	+	0.0229576i	−0.273476	+	0.961879i	$0.588173\pi$
$660$		0			0
$661$	2.24221	−	10.5488i	0.0872120	−	0.410300i	−0.912786	−	0.408437i	$-0.866074\pi$
$661$	2.24221	−	10.5488i	0.0872120	−	0.410300i	0.999998	−	0.00186255i	$-0.000592870\pi$
$662$	0.280953	−	5.36090i	0.0109195	−	0.208357i
$663$	46.4453	+	30.1619i	1.80379	+	1.17139i
$664$	1.94553	+	5.98771i	0.0755010	+	0.232368i
$665$		0			0
$666$	1.42229	−	4.37734i	0.0551124	−	0.169619i
$667$	−1.24614	+	1.00910i	−0.0482507	+	0.0390727i
$668$	−36.4738	+	9.77313i	−1.41121	+	0.378134i
$669$	21.5776	+	48.4640i	0.834238	+	1.87373i
$670$		0			0
$671$	−8.09687	−	11.1444i	−0.312576	−	0.430224i
$672$	−13.6768	+	15.1695i	−0.527595	+	0.585177i
$673$	39.2085	+	19.9777i	1.51138	+	0.770084i	0.996208	−	0.0870048i	$-0.0277296\pi$
$673$	39.2085	+	19.9777i	1.51138	+	0.770084i	0.515168	+	0.857089i	$0.327730\pi$
$674$	3.14838	−	1.81772i	0.121271	−	0.0700159i
$675$		0			0
$676$	−0.455616	+	0.789150i	−0.0175237	+	0.0303519i
$677$	−0.476818	−	9.09823i	−0.0183256	−	0.349674i	−0.992368	−	0.123309i	$-0.960649\pi$
$677$	−0.476818	−	9.09823i	−0.0183256	−	0.349674i	0.974043	−	0.226364i	$-0.0726840\pi$
$678$	−5.27157	−	0.834934i	−0.202453	−	0.0320655i
$679$	−12.2557	+	24.0141i	−0.470332	+	0.921576i
$680$		0			0
$681$	3.93239	−	37.4141i	0.150689	−	1.43371i
$682$	0.301210	+	1.12413i	0.0115339	+	0.0430452i
$683$	−10.0618	+	26.2120i	−0.385006	+	1.00297i	0.594951	+	0.803762i	$0.297172\pi$
$683$	−10.0618	+	26.2120i	−0.385006	+	1.00297i	−0.979956	+	0.199212i	$0.936162\pi$
$684$	52.4026	−	11.1385i	2.00366	−	0.425892i
$685$		0			0
$686$	−3.06303	−	3.79786i	−0.116947	−	0.145003i
$687$	45.6248	−	23.2470i	1.74069	−	0.886927i
$688$	−15.6221	+	24.0559i	−0.595586	+	0.917122i
$689$	10.6320	+	2.25989i	0.405046	+	0.0860951i
$690$		0			0
$691$	10.4802	+	49.3056i	0.398686	+	1.87567i	0.477257	+	0.878764i	$0.341631\pi$
$691$	10.4802	+	49.3056i	0.398686	+	1.87567i	−0.0785710	+	0.996909i	$0.525036\pi$
$692$	−16.0133	+	2.53626i	−0.608735	+	0.0964141i
$693$	−10.2182	+	31.3780i	−0.388158	+	1.19195i
$694$	−0.389209	+	0.535701i	−0.0147742	+	0.0203349i
$695$		0			0
$696$	−0.660865	+	0.0694597i	−0.0250500	+	0.00263286i
$697$	2.21217	−	2.73180i	0.0837917	−	0.103474i
$698$	7.30010	−	0.382582i	0.276313	−	0.0144809i
$699$	−17.4884			−0.661473
$700$		0			0
$701$	−10.4471			−0.394583			−0.197292	−	0.980345i	$-0.563215\pi$
$701$	−10.4471			−0.394583			−0.197292	+	0.980345i	$0.563215\pi$
$702$	−1.35942	+	0.0712443i	−0.0513081	+	0.00268894i
$703$	−24.2083	+	29.8948i	−0.913035	+	1.12750i
$704$	22.3000	−	2.34383i	0.840464	−	0.0883363i
$705$		0			0
$706$	3.77988	−	5.20256i	0.142258	−	0.195801i
$707$	19.1751	+	21.3244i	0.721154	+	0.801986i
$708$	27.2528	−	4.31641i	1.02422	−	0.162221i
$709$	2.36320	+	11.1180i	0.0887517	+	0.417544i	0.999984	+	0.00565112i	$0.00179882\pi$
$709$	2.36320	+	11.1180i	0.0887517	+	0.417544i	−0.911232	+	0.411893i	$0.864868\pi$
$710$		0			0
$711$	−34.1811	−	7.26543i	−1.28189	−	0.272475i
$712$	2.16939	−	3.34056i	0.0813012	−	0.125193i
$713$	7.16432	−	3.65040i	0.268306	−	0.136709i
$714$	2.71522	+	10.1601i	0.101615	+	0.380233i
$715$		0			0
$716$	−29.0215	+	6.16871i	−1.08458	+	0.230535i
$717$	−3.92610	+	10.2279i	−0.146623	+	0.381966i
$718$	−2.46843	−	9.21230i	−0.0921209	−	0.343800i
$719$	4.58882	−	43.6597i	0.171134	−	1.62823i	−0.485650	−	0.874153i	$-0.661417\pi$
$719$	4.58882	−	43.6597i	0.171134	−	1.62823i	0.656784	−	0.754078i	$-0.271916\pi$
$720$		0			0
$721$	−0.674108	−	13.0271i	−0.0251051	−	0.485154i
$722$	10.9546	+	1.73505i	0.407690	+	0.0645717i
$723$	0.490146	+	9.35255i	0.0182287	+	0.347825i
$724$	7.46696	−	12.9332i	0.277507	−	0.480657i
$725$		0			0
$726$	−0.784728	+	0.453063i	−0.0291240	+	0.0168147i
$727$	−29.7714	−	15.1693i	−1.10416	−	0.562598i	−0.195740	−	0.980656i	$-0.562711\pi$
$727$	−29.7714	−	15.1693i	−1.10416	−	0.562598i	−0.908420	+	0.418058i	$0.862711\pi$
$728$	−9.56573	+	3.10112i	−0.354529	+	0.114935i
$729$	−21.0586	−	28.9847i	−0.779949	−	1.07351i
$730$		0			0
$731$	19.1671	+	43.0499i	0.708919	+	1.59226i
$732$	−18.7124	+	5.01398i	−0.691631	+	0.185322i
$733$	−29.5521	+	23.9308i	−1.09153	+	0.883904i	−0.993786	−	0.111307i	$-0.964496\pi$
$733$	−29.5521	+	23.9308i	−1.09153	+	0.883904i	−0.0977448	+	0.995212i	$0.531163\pi$
$734$	0.961845	−	2.96026i	0.0355024	−	0.109265i
$735$		0			0
$736$	5.96087	+	18.3457i	0.219721	+	0.676230i
$737$	3.49366	+	2.26881i	0.128691	+	0.0835726i
$738$	−0.0291854	+	0.556892i	−0.00107433	+	0.0204995i
$739$	−6.32030	+	29.7347i	−0.232496	+	1.09381i	0.694720	+	0.719281i	$0.255528\pi$
$739$	−6.32030	+	29.7347i	−0.232496	+	1.09381i	−0.927216	+	0.374528i	$0.877805\pi$
$740$		0			0
$741$	69.8339	+	22.6904i	2.56541	+	0.833553i
$742$	1.21217	+	1.67072i	0.0445000	+	0.0613340i
$743$	8.10749	−	8.10749i	0.297435	−	0.297435i	−0.542573	−	0.840008i	$-0.682550\pi$
$743$	8.10749	−	8.10749i	0.297435	−	0.297435i	0.840008	+	0.542573i	$0.182550\pi$
$744$	3.31392	+	0.348307i	0.121494	+	0.0127696i
$745$		0			0
$746$	−0.545955	−	5.19442i	−0.0199888	−	0.190181i
$747$	20.1507	−	7.73511i	0.737274	−	0.283013i
$748$	18.1542	−	35.6295i	0.663781	−	1.30274i
$749$	−12.4435	+	19.1337i	−0.454676	+	0.699130i
$750$		0			0
$751$	−22.9279	−	39.7123i	−0.836652	−	1.44912i	−0.892678	−	0.450694i	$-0.851176\pi$
$751$	−22.9279	−	39.7123i	−0.836652	−	1.44912i	0.0560263	−	0.998429i	$-0.482157\pi$
$752$	3.15991	−	2.05207i	0.115230	−	0.0748313i
$753$	−46.2474	−	37.4504i	−1.68535	−	1.36477i
$754$	−0.221495	−	0.0986157i	−0.00806636	−	0.00359137i
$755$		0			0
$756$	5.58534	+	4.52902i	0.203137	+	0.164719i
$757$	24.8825	+	24.8825i	0.904371	+	0.904371i	0.995811	−	0.0914400i	$-0.0291470\pi$
$757$	24.8825	+	24.8825i	0.904371	+	0.904371i	−0.0914400	+	0.995811i	$0.529147\pi$
$758$	−2.46071	−	3.03873i	−0.0893771	−	0.110372i
$759$	38.4771	+	42.7332i	1.39663	+	1.55112i
$760$		0			0
$761$	−18.8581	−	16.9799i	−0.683606	−	0.615522i	0.252351	−	0.967636i	$-0.418796\pi$
$761$	−18.8581	−	16.9799i	−0.683606	−	0.615522i	−0.935957	+	0.352114i	$0.885463\pi$
$762$	3.00963	+	5.90674i	0.109028	+	0.213979i
$763$	21.0581	−	9.35902i	0.762353	−	0.338819i
$764$	−12.6904	+	4.12337i	−0.459124	+	0.149178i
$765$		0			0
$766$	−5.55336	+	5.00027i	−0.200651	+	0.180667i
$767$	19.1357	+	7.34550i	0.690950	+	0.265231i
$768$	7.10883	−	26.5305i	0.256518	−	0.957338i
$769$	−8.55473	−	6.21537i	−0.308491	−	0.224132i	0.422757	−	0.906243i	$-0.361062\pi$
$769$	−8.55473	−	6.21537i	−0.308491	−	0.224132i	−0.731249	+	0.682111i	$0.761062\pi$
$770$		0			0
$771$	−0.672540	+	0.488629i	−0.0242209	+	0.0175975i
$772$	6.83310	+	17.8008i	0.245929	+	0.640666i
$773$	−3.89062	−	5.99102i	−0.139936	−	0.215482i	0.761753	−	0.647867i	$-0.224339\pi$
$773$	−3.89062	−	5.99102i	−0.139936	−	0.215482i	−0.901689	+	0.432385i	$0.857672\pi$
$774$	−6.47431	−	3.73794i	−0.232714	−	0.134358i
$775$		0			0
$776$			10.5520i			0.378796i
$777$	−33.3230	−	0.0219716i	−1.19546	−	0.000788227i
$778$	−0.850924	+	5.37252i	−0.0305071	+	0.192614i
$779$	1.89569	−	4.25780i	0.0679203	−	0.152552i
$780$		0			0
$781$	−28.3072	+	12.6032i	−1.01291	+	0.450976i
$782$	9.59386	+	2.57067i	0.343076	+	0.0919268i
$783$	0.0552195	+	0.348642i	0.00197339	+	0.0124595i
$784$	22.9336	+	10.2470i	0.819057	+	0.365963i
$785$		0			0
$786$	6.13479	−	6.81337i	0.218821	−	0.243025i
$787$	12.8429	+	0.673066i	0.457799	+	0.0239922i	0.279842	−	0.960046i	$-0.409718\pi$
$787$	12.8429	+	0.673066i	0.457799	+	0.0239922i	0.177957	+	0.984038i	$0.443051\pi$
$788$	11.4347	+	0.599270i	0.407346	+	0.0213481i
$789$	11.5684	−	12.8480i	0.411847	−	0.457402i
$790$		0			0
$791$	3.26266	+	20.6879i	0.116007	+	0.735576i
$792$	2.02045	+	12.7566i	0.0717937	+	0.453288i
$793$	−13.9005	−	3.72464i	−0.493623	−	0.132266i
$794$	0.253422	−	0.112831i	0.00899359	−	0.00400421i
$795$		0			0
$796$	1.11594	−	2.50644i	0.0395535	−	0.0888386i
$797$	−2.58451	+	16.3180i	−0.0915481	+	0.578012i	0.898685	+	0.438594i	$0.144523\pi$
$797$	−2.58451	+	16.3180i	−0.0915481	+	0.578012i	−0.990234	+	0.139418i	$0.955477\pi$
$798$	6.96405	+	12.0805i	0.246525	+	0.427644i
$799$		−	6.19008i		−	0.218989i
$800$		0			0
$801$	−11.8261	−	6.82780i	−0.417855	−	0.241249i
$802$	−0.0530501	−	0.0816900i	−0.00187326	−	0.00288457i
$803$	−10.0939	−	26.2954i	−0.356205	−	0.927946i
$804$	4.73952	−	3.44346i	0.167150	−	0.121442i
$805$		0			0
$806$	0.983605	+	0.714631i	0.0346460	+	0.0251718i
$807$	0.386077	−	1.44086i	0.0135905	−	0.0507206i
$808$	10.4786	+	4.02234i	0.368634	+	0.141506i
$809$	27.9141	−	25.1340i	0.981407	−	0.883663i	−0.0118109	−	0.999930i	$-0.503760\pi$
$809$	27.9141	−	25.1340i	0.981407	−	0.883663i	0.993218	+	0.116267i	$0.0370929\pi$
$810$		0			0
$811$	−19.9913	+	6.49556i	−0.701989	+	0.228090i	−0.638197	−	0.769873i	$-0.720319\pi$
$811$	−19.9913	+	6.49556i	−0.701989	+	0.228090i	−0.0637922	+	0.997963i	$0.520319\pi$
$812$	0.520153	+	1.17036i	0.0182538	+	0.0410716i
$813$	−21.5869	−	42.3667i	−0.757086	−	1.48587i
$814$	−3.38507	−	3.04793i	−0.118647	−	0.106830i
$815$		0			0
$816$	−36.2280	−	40.2353i	−1.26823	−	1.40852i
$817$	39.3209	+	48.5573i	1.37566	+	1.69880i
$818$	5.46627	+	5.46627i	0.191124	+	0.191124i
$819$	12.3334	+	32.1931i	0.430965	+	1.12492i
$820$		0			0
$821$	−45.0953	−	20.0777i	−1.57384	−	0.700718i	−0.580320	−	0.814389i	$-0.697072\pi$
$821$	−45.0953	−	20.0777i	−1.57384	−	0.700718i	−0.993518	+	0.113671i	$0.963739\pi$
$822$	−3.19584	−	2.58794i	−0.111468	−	0.0902648i
$823$	43.6298	−	28.3335i	1.52084	−	0.987645i	0.530701	−	0.847559i	$-0.321929\pi$
$823$	43.6298	−	28.3335i	1.52084	−	0.987645i	0.990139	−	0.140086i	$-0.0447380\pi$
$824$	−2.55272	−	4.42144i	−0.0889282	−	0.154028i
$825$		0			0
$826$	1.76484	+	3.46935i	0.0614066	+	0.120714i
$827$	−17.1839	+	33.7254i	−0.597544	+	1.17275i	0.372093	+	0.928196i	$0.378640\pi$
$827$	−17.1839	+	33.7254i	−0.597544	+	1.17275i	−0.969637	+	0.244550i	$0.921360\pi$
$828$	40.9187	−	15.7072i	1.42202	−	0.545864i
$829$	−3.99905	−	38.0484i	−0.138893	−	1.32147i	−0.812750	−	0.582613i	$-0.802030\pi$
$829$	−3.99905	−	38.0484i	−0.138893	−	1.32147i	0.673857	−	0.738862i	$-0.264636\pi$
$830$		0			0
$831$	−3.82326	−	0.401841i	−0.132628	−	0.0139397i
$832$	16.5640	−	16.5640i	0.574254	−	0.574254i
$833$	34.6396	−	22.4303i	1.20019	−	0.777164i
$834$	0.274207	+	0.0890952i	0.00949500	+	0.00308511i
$835$		0			0
$836$	11.0234	−	51.8612i	0.381254	−	1.79366i
$837$	0.0926383	−	1.76764i	0.00320205	−	0.0610987i
$838$	−1.89843	−	1.23286i	−0.0655802	−	0.0425883i
$839$	5.99213	+	18.4419i	0.206871	+	0.636684i	0.999631	+	0.0271505i	$0.00864335\pi$
$839$	5.99213	+	18.4419i	0.206871	+	0.636684i	−0.792760	+	0.609534i	$0.791357\pi$
$840$		0			0
$841$	8.94206	−	27.5208i	0.308347	−	0.948995i
$842$	−6.55174	+	5.30550i	−0.225788	+	0.182840i
$843$	73.9707	−	19.8204i	2.54769	−	0.682651i
$844$	−10.5500	−	23.6957i	−0.363146	−	0.815639i
$845$		0			0
$846$	0.577212	+	0.794464i	0.0198449	+	0.0273142i
$847$	2.64080	+	2.38094i	0.0907388	+	0.0818100i
$848$	−9.46833	−	4.82435i	−0.325144	−	0.165669i
$849$	−19.9110	+	11.4956i	−0.683342	+	0.394528i
$850$		0			0
$851$	−15.7357	+	27.2550i	−0.539411	+	0.934288i
$852$	2.28062	+	43.5169i	0.0781329	+	1.49086i
$853$	−9.23966	−	1.46342i	−0.316360	−	0.0501065i	−0.00376463	−	0.999993i	$-0.501198\pi$
$853$	−9.23966	−	1.46342i	−0.316360	−	0.0501065i	−0.312595	+	0.949886i	$0.601198\pi$
$854$	−1.48691	−	2.29295i	−0.0508809	−	0.0784630i
$855$		0			0
$856$	−0.933754	+	8.88408i	−0.0319151	+	0.303652i
$857$	4.23294	+	15.7975i	0.144594	+	0.539633i	0.999773	+	0.0213003i	$0.00678061\pi$
$857$	4.23294	+	15.7975i	0.144594	+	0.539633i	−0.855179	+	0.518333i	$0.826553\pi$
$858$	−3.11595	+	8.11731i	−0.106377	+	0.277121i
$859$	47.3304	−	10.0604i	1.61489	−	0.343256i	0.690096	−	0.723717i	$-0.257568\pi$
$859$	47.3304	−	10.0604i	1.61489	−	0.343256i	0.924797	+	0.380461i	$0.124235\pi$
$860$		0			0
$861$	3.90056	−	1.04239i	0.132931	−	0.0355247i
$862$	−7.34193	+	3.74090i	−0.250067	+	0.127416i
$863$	−28.6272	+	44.0820i	−0.974481	+	1.50057i	−0.112485	+	0.993653i	$0.535881\pi$
$863$	−28.6272	+	44.0820i	−0.974481	+	1.50057i	−0.861996	+	0.506916i	$0.830786\pi$
$864$	4.15363	+	0.882882i	0.141309	+	0.0300362i
$865$		0			0
$866$	−0.0932651	−	0.438778i	−0.00316928	−	0.0149103i
$867$	−44.8823	+	7.10866i	−1.52428	+	0.241423i
$868$	−1.33113	−	6.28285i	−0.0451816	−	0.213254i
$869$	−20.3278	+	27.9788i	−0.689574	+	0.949117i
$870$		0			0
$871$	4.32806	−	0.454897i	0.146651	−	0.0154136i
$872$	5.67593	−	7.00919i	0.192211	−	0.237361i
$873$	36.1263	−	1.89330i	1.22269	−	0.0640784i
$874$	13.1692			0.445454
$875$		0			0
$876$	−39.6110			−1.33833
$877$	27.2293	−	1.42703i	0.919469	−	0.0481873i	0.413274	−	0.910607i	$-0.364385\pi$
$877$	27.2293	−	1.42703i	0.919469	−	0.0481873i	0.506195	+	0.862419i	$0.331052\pi$
$878$	4.92988	−	6.08790i	0.166375	−	0.205457i
$879$	−70.5293	+	7.41293i	−2.37890	+	0.250032i
$880$		0			0
$881$	−0.398014	+	0.547820i	−0.0134094	+	0.0184565i	−0.815669	−	0.578519i	$-0.803631\pi$
$881$	−0.398014	+	0.547820i	−0.0134094	+	0.0184565i	0.802260	+	0.596975i	$0.203631\pi$
$882$	−2.35423	+	6.10888i	−0.0792709	+	0.205697i
$883$	31.4097	−	4.97481i	1.05702	−	0.167416i	0.396356	−	0.918097i	$-0.370274\pi$
$883$	31.4097	−	4.97481i	1.05702	−	0.167416i	0.660665	+	0.750681i	$0.270274\pi$
$884$	−8.68556	−	40.8623i	−0.292127	−	1.37435i
$885$		0			0
$886$	−6.47597	−	1.37651i	−0.217565	−	0.0462448i
$887$	0.370913	−	0.571156i	0.0124540	−	0.0191775i	−0.832389	−	0.554192i	$-0.813027\pi$
$887$	0.370913	−	0.571156i	0.0124540	−	0.0191775i	0.844843	+	0.535015i	$0.179694\pi$
$888$	−11.6206	+	5.92101i	−0.389963	+	0.198696i
$889$	18.4064	−	18.3821i	0.617331	−	0.616517i
$890$		0			0
$891$	−24.2186	+	5.14782i	−0.811353	+	0.172458i
$892$	14.3412	−	37.3602i	0.480180	−	1.25091i
$893$	−2.12423	−	7.92774i	−0.0710847	−	0.265292i
$894$	−0.226534	+	2.15533i	−0.00757643	+	0.0720849i
$895$		0			0
$896$	20.3823	−	1.05472i	0.680926	−	0.0352356i
$897$	59.3337	+	9.39753i	1.98109	+	0.313774i
$898$	0.269574	+	5.14377i	0.00899579	+	0.171650i
$899$	0.157632	−	0.273026i	0.00525731	−	0.00910592i
$900$		0			0
$901$	−15.1194	+	8.72921i	−0.503701	+	0.290812i
$902$	0.491742	+	0.250555i	0.0163732	+	0.00834256i
$903$	−11.2882	+	52.9354i	−0.375649	+	1.76158i
$904$	4.81808	+	6.63152i	0.160247	+	0.220561i
$905$		0			0
$906$	1.50206	+	3.37368i	0.0499025	+	0.112083i
$907$	42.2126	−	11.3108i	1.40165	−	0.375570i	0.522710	−	0.852510i	$-0.324921\pi$
$907$	42.2126	−	11.3108i	1.40165	−	0.375570i	0.878936	+	0.476941i	$0.158254\pi$
$908$	−22.0543	+	17.8592i	−0.731896	+	0.592678i
$909$	11.8909	−	36.5965i	0.394397	−	1.21383i
$910$		0			0
$911$	−8.28755	−	25.5065i	−0.274579	−	0.845067i	−0.989331	−	0.145689i	$-0.953460\pi$
$911$	−8.28755	−	25.5065i	−0.274579	−	0.845067i	0.714752	−	0.699378i	$-0.246540\pi$
$912$	−60.2053	−	39.0978i	−1.99360	−	1.29466i
$913$	1.11796	−	21.3320i	0.0369992	−	0.705986i
$914$	−0.345590	+	1.62587i	−0.0114311	+	0.0537791i
$915$		0			0
$916$	−36.7362	−	11.9363i	−1.21380	−	0.394387i
$917$	−32.8565	−	14.6546i	−1.08502	−	0.483939i
$918$	1.54608	−	1.54608i	0.0510281	−	0.0510281i
$919$	43.3179	+	4.55289i	1.42892	+	0.150186i	0.787176	−	0.616729i	$-0.211542\pi$
$919$	43.3179	+	4.55289i	1.42892	+	0.150186i	0.641749	+	0.766915i	$0.278209\pi$
$920$		0			0
$921$	1.82039	+	17.3198i	0.0599838	+	0.570707i
$922$	−1.30974	+	0.502761i	−0.0431339	+	0.0165575i
$923$	−14.6961	+	28.8427i	−0.483728	+	0.949370i
$924$	40.9370	−	20.8245i	1.34673	−	0.685074i
$925$		0			0
$926$	−2.92866	−	5.07259i	−0.0962417	−	0.166696i
$927$	−14.6794	+	9.53289i	−0.482134	+	0.313101i
$928$	0.587772	+	0.475969i	0.0192946	+	0.0156244i
$929$	−38.1215	−	16.9728i	−1.25073	−	0.556859i	−0.328863	−	0.944378i	$-0.606666\pi$
$929$	−38.1215	−	16.9728i	−1.25073	−	0.556859i	−0.921862	+	0.387519i	$0.873332\pi$
$930$		0			0
$931$	36.6661	−	40.6140i	1.20168	−	1.33107i
$932$	9.32834	+	9.32834i	0.305560	+	0.305560i
$933$	−49.0800	−	60.6088i	−1.60681	−	1.98424i
$934$	1.31181	+	1.45691i	0.0429237	+	0.0476716i
$935$		0			0
$936$	10.0272	+	9.02853i	0.327749	+	0.295107i
$937$	9.28106	+	18.2151i	0.303199	+	0.595062i	0.991461	−	0.130400i	$-0.0416262\pi$
$937$	9.28106	+	18.2151i	0.303199	+	0.595062i	−0.688262	+	0.725462i	$0.741626\pi$
$938$	0.668277	+	0.486205i	0.0218200	+	0.0158752i
$939$	30.2459	−	9.82748i	0.987037	−	0.320708i
$940$		0			0
$941$	−2.78647	+	2.50895i	−0.0908362	+	0.0817893i	−0.713298	−	0.700861i	$-0.752799\pi$
$941$	−2.78647	+	2.50895i	−0.0908362	+	0.0817893i	0.622462	+	0.782650i	$0.286133\pi$
$942$	−12.7523	−	4.89515i	−0.415492	−	0.159493i
$943$	0.986899	−	3.68316i	0.0321379	−	0.119940i
$944$	−16.2119	−	11.7786i	−0.527652	−	0.383361i
$945$		0			0
$946$	−5.98563	+	4.34882i	−0.194610	+	0.141392i
$947$	−19.6429	−	51.1715i	−0.638308	−	1.66285i	−0.743778	−	0.668427i	$-0.766968\pi$
$947$	−19.6429	−	51.1715i	−0.638308	−	1.66285i	0.105470	−	0.994423i	$-0.466365\pi$
$948$	26.4892	+	40.7898i	0.860328	+	1.32479i
$949$	−25.4829	−	14.7126i	−0.827210	−	0.477590i
$950$		0			0
$951$			7.04452i			0.228434i
$952$	8.08500	−	13.9823i	0.262036	−	0.453170i
$953$	3.77491	−	23.8338i	0.122281	−	0.772054i	−0.847986	−	0.530019i	$-0.822185\pi$
$953$	3.77491	−	23.8338i	0.122281	−	0.772054i	0.970267	−	0.242036i	$-0.0778151\pi$
$954$	1.12652	−	2.53020i	0.0364724	−	0.0819183i
$955$		0			0
$956$	7.54972	−	3.36135i	0.244176	−	0.108714i
$957$	2.17778	+	0.583535i	0.0703977	+	0.0188630i
$958$	−0.523200	−	3.30335i	−0.0169038	−	0.106727i
$959$	−5.79279	+	15.0610i	−0.187059	+	0.486346i
$960$		0			0
$961$	19.6852	−	21.8627i	0.635007	−	0.705247i
$962$	−4.75213	−	0.249048i	−0.153215	−	0.00802965i
$963$	30.5834	+	1.60281i	0.985535	+	0.0516497i
$964$	4.72721	−	5.25010i	0.152253	−	0.169094i
$965$		0			0
$966$	7.17344	+	8.87042i	0.230802	+	0.285401i
$967$	−0.694147	−	4.38267i	−0.0223222	−	0.140937i	0.974010	−	0.226504i	$-0.0727298\pi$
$967$	−0.694147	−	4.38267i	−0.0223222	−	0.140937i	−0.996332	+	0.0855672i	$0.972730\pi$
$968$	1.34421	+	0.360181i	0.0432046	+	0.0115766i
$969$	−107.742	+	47.9699i	−3.46118	+	1.54102i
$970$		0			0
$971$	−1.14821	+	2.57893i	−0.0368479	+	0.0827617i	−0.931032	−	0.364938i	$-0.881090\pi$
$971$	−1.14821	+	2.57893i	−0.0368479	+	0.0827617i	0.894184	+	0.447700i	$0.147757\pi$
$972$	−6.72260	+	42.4448i	−0.215627	+	1.36142i
$973$	0.000745968	−	1.13136i	2.39146e−5	−	0.0362699i
$974$			4.13304i			0.132431i
$975$		0			0
$976$	12.1843	+	7.03463i	0.390011	+	0.225173i
$977$	−12.4592	−	19.1854i	−0.398604	−	0.613797i	0.581199	−	0.813762i	$-0.302584\pi$
$977$	−12.4592	−	19.1854i	−0.398604	−	0.613797i	−0.979803	+	0.199965i	$0.935917\pi$
$978$	−2.10355	−	5.47994i	−0.0672642	−	0.175229i
$979$	−10.9335	+	7.94364i	−0.349436	+	0.253880i
$980$		0			0
$981$	−25.0153	−	18.1747i	−0.798677	−	0.580273i
$982$	−0.978710	+	3.65259i	−0.0312319	+	0.116559i
$983$	25.3059	+	9.71403i	0.807133	+	0.309829i	0.726721	−	0.686932i	$-0.241043\pi$
$983$	25.3059	+	9.71403i	0.807133	+	0.309829i	0.0804117	+	0.996762i	$0.474377\pi$
$984$	1.17431	−	1.05736i	0.0374358	−	0.0337073i
$985$		0			0
$986$	0.370369	−	0.120340i	0.0117950	−	0.00383241i
$987$	4.18282	−	5.74918i	0.133141	−	0.182998i
$988$	−25.1463	−	49.3525i	−0.800012	−	1.57011i
$989$	37.9880	+	34.2046i	1.20795	+	1.08764i
$990$		0			0
$991$	11.0607	+	12.2841i	0.351354	+	0.390219i	0.892752	−	0.450548i	$-0.148771\pi$
$991$	11.0607	+	12.2841i	0.351354	+	0.390219i	−0.541398	+	0.840767i	$0.682105\pi$
$992$	−2.38676	−	2.94740i	−0.0757796	−	0.0935800i
$993$	36.8761	+	36.8761i	1.17023	+	1.17023i
$994$	−5.74045	+	2.19921i	−0.182076	+	0.0697547i
$995$		0			0
$996$	−27.4439	−	12.2188i	−0.869592	−	0.387167i
$997$	2.37413	+	1.92253i	0.0751895	+	0.0608872i	0.666178	−	0.745792i	$-0.267929\pi$
$997$	2.37413	+	1.92253i	0.0751895	+	0.0608872i	−0.590989	+	0.806680i	$0.701262\pi$
$998$	−1.70519	+	1.10736i	−0.0539767	+	0.0350529i
$999$	3.46403	+	5.99987i	0.109597	+	0.189827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.b.857.9		288
5.2	odd	4		875.2.bb.c.143.9		288
5.3	odd	4		175.2.x.a.108.10	yes	288
5.4	even	2		875.2.bb.a.857.10		288
7.5	odd	6	inner	875.2.bb.b.607.10		288
25.3	odd	20	inner	875.2.bb.b.493.10		288
25.4	even	10		875.2.bb.c.507.9		288
25.21	even	5		175.2.x.a.122.10	yes	288
25.22	odd	20		875.2.bb.a.493.9		288
35.12	even	12		875.2.bb.c.768.9		288
35.19	odd	6		875.2.bb.a.607.9		288
35.33	even	12		175.2.x.a.33.10	✓	288
175.47	even	60		875.2.bb.a.243.10		288
175.54	odd	30		875.2.bb.c.257.9		288
175.96	odd	30		175.2.x.a.47.10	yes	288
175.103	even	60	inner	875.2.bb.b.243.9		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.10	✓	288	35.33	even	12
175.2.x.a.47.10	yes	288	175.96	odd	30
175.2.x.a.108.10	yes	288	5.3	odd	4
175.2.x.a.122.10	yes	288	25.21	even	5
875.2.bb.a.243.10		288	175.47	even	60
875.2.bb.a.493.9		288	25.22	odd	20
875.2.bb.a.607.9		288	35.19	odd	6
875.2.bb.a.857.10		288	5.4	even	2
875.2.bb.b.243.9		288	175.103	even	60	inner
875.2.bb.b.493.10		288	25.3	odd	20	inner
875.2.bb.b.607.10		288	7.5	odd	6	inner
875.2.bb.b.857.9		288	1.1	even	1	trivial
875.2.bb.c.143.9		288	5.2	odd	4
875.2.bb.c.257.9		288	175.54	odd	30
875.2.bb.c.507.9		288	25.4	even	10
875.2.bb.c.768.9		288	35.12	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.263087 + 0.0137878i) q^{2} +(1.61063 - 1.98896i) q^{3} +(-1.92002 + 0.201802i) q^{4} +(-0.396312 + 0.545476i) q^{6} +(2.51572 + 0.819241i) q^{7} +(1.02276 - 0.161989i) q^{8} +(-0.738101 - 3.47249i) q^{9} +(-3.43661 - 0.730475i) q^{11} +(-2.69106 + 4.14386i) q^{12} +(-3.27037 + 1.66634i) q^{13} +(-0.673149 - 0.180846i) q^{14} +(3.50997 - 0.746068i) q^{16} +(2.11271 - 5.50381i) q^{17} +(0.242063 + 0.903391i) q^{18} +(0.817063 - 7.77383i) q^{19} +(5.68132 - 3.68417i) q^{21} +(0.914201 + 0.144795i) q^{22} +(-0.334690 - 6.38626i) q^{23} +(1.32509 - 2.29513i) q^{24} +(0.837417 - 0.483483i) q^{26} +(-1.25435 - 0.639125i) q^{27} +(-4.99555 - 1.06528i) q^{28} +(-0.147381 - 0.202852i) q^{29} +(0.511405 + 1.14863i) q^{31} +(-2.91359 + 0.780694i) q^{32} +(-6.98798 + 5.65876i) q^{33} +(-0.479943 + 1.47711i) q^{34} +(2.11792 + 6.51830i) q^{36} +(-4.12728 - 2.68029i) q^{37} +(-0.107775 + 2.05646i) q^{38} +(-1.95307 + 9.18847i) q^{39} +(0.567075 + 0.184254i) q^{41} +(-1.44389 + 1.04759i) q^{42} +(-5.65218 + 5.65218i) q^{43} +(6.74578 + 0.709010i) q^{44} +(0.176105 + 1.67553i) q^{46} +(0.980249 - 0.376282i) q^{47} +(4.16936 - 8.18282i) q^{48} +(5.65769 + 4.12196i) q^{49} +(-7.54405 - 13.0667i) q^{51} +(5.94290 - 3.85937i) q^{52} +(-2.30142 - 1.86365i) q^{53} +(0.338816 + 0.150851i) q^{54} +(2.70568 + 0.430367i) q^{56} +(-14.1458 - 14.1458i) q^{57} +(0.0415708 + 0.0513357i) q^{58} +(-3.73669 - 4.15002i) q^{59} +(2.91370 + 2.62351i) q^{61} +(-0.150381 - 0.295140i) q^{62} +(0.987952 - 9.34049i) q^{63} +(-6.06975 + 1.97218i) q^{64} +(1.76043 - 1.58510i) q^{66} +(-1.10691 - 0.424905i) q^{67} +(-2.94577 + 10.9938i) q^{68} +(-13.2411 - 9.62020i) q^{69} +(7.13505 - 5.18392i) q^{71} +(-1.31741 - 3.43196i) q^{72} +(4.36627 + 6.72347i) q^{73} +(1.12279 + 0.648243i) q^{74} +15.0908i q^{76} +(-8.04712 - 4.65309i) q^{77} +(0.387139 - 2.44430i) q^{78} +(4.00368 - 8.99240i) q^{79} +(6.43796 - 2.86636i) q^{81} +(-0.151731 - 0.0406561i) q^{82} +(0.951116 + 6.00511i) q^{83} +(-10.1648 + 8.22017i) q^{84} +(1.40908 - 1.56495i) q^{86} +(-0.640839 - 0.0335849i) q^{87} +(-3.63316 - 0.190406i) q^{88} +(2.57386 - 2.85856i) q^{89} +(-9.59246 + 1.51281i) q^{91} +(1.93137 + 12.1942i) q^{92} +(3.10827 + 0.832857i) q^{93} +(-0.252703 + 0.112511i) q^{94} +(-3.13994 + 7.05242i) q^{96} +(-1.59410 + 10.0647i) q^{97} +(-1.54530 - 1.00643i) q^{98} +12.4728i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 2 q^{2} + 6 q^{3} + 10 q^{4} - 10 q^{7} + 64 q^{8} + 10 q^{9} - 6 q^{11} - 6 q^{12} + 20 q^{14} - 30 q^{16} - 12 q^{17} - 14 q^{18} + 30 q^{19} - 12 q^{21} - 8 q^{22} + 30 q^{23} - 48 q^{26} - 58 q^{28}+ \cdots + 62 q^{98}+O(q^{100}) \) 288 * q + 2 * q^2 + 6 * q^3 + 10 * q^4 - 10 * q^7 + 64 * q^8 + 10 * q^9 - 6 * q^11 - 6 * q^12 + 20 * q^14 - 30 * q^16 - 12 * q^17 - 14 * q^18 + 30 * q^19 - 12 * q^21 - 8 * q^22 + 30 * q^23 - 48 * q^26 - 58 * q^28 - 18 * q^31 + 8 * q^32 - 150 * q^33 + 40 * q^36 + 12 * q^38 - 30 * q^39 + 166 * q^42 - 108 * q^43 + 10 * q^44 - 6 * q^46 - 24 * q^47 - 16 * q^51 - 24 * q^52 - 40 * q^53 + 30 * q^54 + 4 * q^56 - 216 * q^57 - 114 * q^58 - 90 * q^59 - 18 * q^61 - 16 * q^63 + 100 * q^64 - 90 * q^66 + 74 * q^67 + 342 * q^68 - 24 * q^71 - 222 * q^72 - 216 * q^73 + 90 * q^77 - 32 * q^78 + 10 * q^79 - 10 * q^81 + 216 * q^82 - 20 * q^84 - 6 * q^86 - 18 * q^87 + 58 * q^88 - 120 * q^89 - 12 * q^91 - 24 * q^92 + 106 * q^93 + 30 * q^94 - 90 * q^96 + 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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